One thing that is generally noted about Dante's Commedia - and that is nonetheless often lost in certain specialized readings into the text - is the fact that Dante does not speak only for himself. There are various points of view that Dante needs to address in his work: Dante's own experience of a moral restoration, his personal truth; there is a poetic truth, which is more often left to Virgil, together with the explanation of the infernal ranks; there is a political truth, which falls to major political figures, and personalities of historical significance; and a religious one, which again is not spoken by Dante-character but through various Fathers of the Church, or Beatrice. Eventually, all these "truths", the private one, the political one, the religious one, the divine one, will come together harmoniously; but that's the end of the whole commedia journey.

Keeping this in mind, Dante's personal attitude towards Caesar should not really be taken as a reason for the severe punishment reserved to Brutus and Cassius. It's a matter of political and religious doctrine - and in fact, Dante does not give any special praise to Caesar in his first introduction, which comes from Dante's point of view:

Electra there I saw accompanied

By many, among whom Hector I knew,

Anchises' pious son, and with hawk's eye

Caesar all arm'd, and by Camilla there

Penthesilea. On the other side

Old King Latinus, seated by his child

Lavinia, and that Brutus I beheld,

Who Tarquin chas'd, Lucretia, Cato's wife

Marcia, with Julia and Cornelia there;

And sole apart retir'd, the Soldan fierce.

Then when a little more I rais'd my brow,

I spied the master of the sapient throng,

Seated amid the philosophic train.

Him all admire, all pay him rev'rence due.

There Socrates and Plato both I mark'd,

Nearest to him in rank; Democritus,

Who sets the world at chance, Diogenes,

With Heraclitus, and Empedocles,

And Anaxagoras, and Thales sage,

Zeno, and Dioscorides well read

In nature's secret lore. Orpheus I mark'd

And Linus, Tully and moral Seneca,

Euclid and Ptolemy, Hippocrates,

Galenus, Avicen, and him who made

That commentary vast, Averroes.

There Caesar is just a noble heaten among others. And Dante has no reason to pay much attention to him. To better understand Caesar's importance and central role, it's better to wait for a more advanced explanation - one that could not be given in hell. The VI Canto of Paradise is one of the most significant for that harmonization of political and religious that Dante seeks to achieve. There he meets the Roman Emperor Justinian:

[...] Caesar I was,

And am Justinian; destin'd by the will

Of that prime love, whose influence I feel,

From vain excess to clear th' encumber'd laws.

Justinian, after briefly detailing his role in the history of the Empire and his understanding of the need to return Rome to its rightful place, could see that Dante wasn't sure of how this should shape the relations between Church and Empire, so that he felt compelled

To some addition; that thou well, mayst mark

What reason on each side they have to plead,

By whom that holiest banner is withstood,

Both who pretend its power and who oppose.

And briefly covering the history of Rome, or better the history of the Roman Eagle - the insignia of the Imperial power - he came to the decisive turn in the history of Christendom:

Near the hour, when heav'n was minded

that o'er all the world his own deep calm should brood,

to Caesar's hand did Rome consign it.

Caesar was the first chosen instrument in the establishment of universal Christendom. And those who opposed his action, did in fact oppose the ultimate design of God for mankind. And thus it makes sense to somewhat equate Brutus and Cassius with Judas, in so far as they all acted against God's design for the salvation of men. It's therefore not really Dante's sympathy or not for Caesar as a mere political figure which matters in his collocation, but the realization that for Dante, far from a tyrant, Caesar - with his choice to strengthen and expand the power of Rome and his own - had initiated the formation of the Empire destined to be the agent of the spreading of Christianity.

and what then it wrought

From Var unto the Rhine, saw Isere's flood,

Saw Loire and Seine, and every vale, that fills

The torrent Rhone. What after that it wrought,

When from Ravenna it came forth, and leap'd

The Rubicon, was of so bold a flight,

That tongue nor pen may follow it. Tow'rds Spain

It wheel'd its bands, then tow'rd Dyrrachium smote,

And on Pharsalia with so fierce a plunge,

E'en the warm Nile was conscious to the pang;

Its native shores Antandros, and the streams

Of Simois revisited, and there

Where Hector lies; then ill for Ptolemy

His pennons shook again; lightning thence fell

On Juba; and the next upon your west,

At sound of the Pompeian trump, return'd.

What following and in its next bearer's gripe

It wrought, is now by Cassius and Brutus

Bark'd off in hell, and by Perugia's sons

And Modena's was mourn'd. Hence weepeth still

Sad Cleopatra, who, pursued by it,

Took from the adder black and sudden death.

With him it ran e'en to the Red Sea coast;

With him compos'd the world to such a peace,

That of his temple Janus barr'd the door.

As you can see, all those who opposed this design fell into disgrace - more so those who did so deliberately and through treason.

Even more, explained Justinian, the Roman Empire was always an instrument of a providential design, even when operating apparently against it, for instance in (unwillingly) chastizing both the original sin (through the crucifixion of Jesus) and the "old sin" (that is the betrayal of the Christ, with the desacration of the Temple of Jerusalem).

And, when the Lombard tooth, with fangs impure,

Did gore the bosom of the holy church,

Under its wings victorious, Charlemagne

Sped to her rescue. Judge then for thyself

Of those, whom I erewhile accus'd to thee,

What they are, and how grievous their offending,

Who are the cause of all your ills.

That would be, both the opposing factions of Guelphs and Ghibellines, who refused to accept the necessary harmonious nature of Church and Empire.

[...] The one

Against the universal ensign rears

The yellow lilies, and with partial aim

That to himself the other arrogates:

So that 't is hard to see which more offends.

Be yours, ye Ghibellines, to veil your arts

Beneath another standard: ill is this

Follow'd of him, who severs it and justice:

And let not with his Guelphs the new-crown'd Charles

Assail it, but those talons hold in dread,

Which from a lion of more lofty port

Have rent the easing.

These themes are central to the whole structure of the Commedia and in some way, they gain primacy over any personal republican sympathy of Dante's. Notably though, Dante does not equate the Empire with any political power or government - this equality of Church and Empire only works for the one Church and the one Empire. This is already clear from Justinian objection to the Ghibellines making themselves strong of the Empire's name for their own political interests.

A better understanding of Dante's political vision can be derived from his treaty Monarchia, on the necessity of the Empire, on its "natural right" (a natural right bestowed upon the people of Rome by God, in the choice of Caesar, and confirmed with the subsequent coming of the Christ) and on its non subordination to the Church.

Now, to go deeper into the subject, one needs a much larger familiarity with XIII-XIV Century theology and political doctrine than I can claim; there is certainly room to expand of some of the points you made, and perhaps provide a general review of the way Caesar was understood by Dante's contemporaries. But on the reason why he had such a relevance despite being a pagan and (maybe) a "tyrant", Dante's own text is rather clear.

opus fuit homini duplici directivo secundum duplicem finem: scilicet summo Pontifice, qui secundum revelata humanum genus perduceret ad vitam ecternam, et Imperatore, qui secundum phylosophica documenta genus humanum ad temporalem felicitatem dirigeret.

That men need two guidances according to two different ends: the Pope to lead them to eternal life and the Emperor to lead them to happiness on earth. And Caesar was the first step in providing them with both.