Charles V had personal lands in the lowlands in addition to his Spanish titles and imperial title but that meant that when he abdicated and split his titles up, his brother became emperor while his son became king And that same son gained the lowlands within the Empire. Such is feudal governance.
But in that century between Charles V and the Dutch war for independence, did the Emperors officially recognize that imperial overlordship was gone in favor of the Spanish Crown?
Was there a chance of removing Spanish control but remaining within the Empire? Or was complete separation from any & all the goal?
The premise of your question seems to be based on a 19th century German notion that took the Treaty of Westphalia as the official or de jure transfer of sovereignty from the Holy Roman Empire. The Peace of Westphalia wasn't viewed as being particularly positive by German historians at the time, who saw it as the closing act of the Thirty Years War, which had destroyed much of what is now Germany. To German school children up until the second half of the 20th century, the Peace of Westphalia was the treaty in which the weakened empire lost Switzerland and the Low Countries.
The idea that Dutch independence was somehow accorded by the Holy Roman Emperor in 1648 or that sovereignty was officially transferred is however completely false. In fact, the stipulations of the Peace of Münster (which constituted one of the two treaties collectively known as the Peace of Westphalia) do not even mention the Holy Roman Empire or Emperor in any form, shape or way.
In reality, the Low Countries started to go their separate ways during the 14th century, when the dukes of Burgundy started to acquire evermore lands in the Low Countries; becoming immensely powerful and effectively forming a de facto "Middle Kingdom" between France and the Holy Roman Empire for some time. The Burgundian treaty of 1548 formalized what had been common practice for quite some time: paying off the Emperor to stay out of their business. Emperor Charles V., himself a Burgundian, essentially separated the Low Countries from the Holy Roman Empire in all but name. In exchange Burgundy paid the taxes equivalent to about 2/3 Prince Electorates, of which there were only 7. The Pragmatic Sanction of 1549 went a step further, by making the Low Countries one indivisible territory, becoming the Seventeen Provinces and eventually (in 1556) being inherited by Charles V's son Philip II, who was also the King of Spain.
The only (legal) way in which the Low Countries could have again formed a part of the Holy Roman Empire, would have been if the owner (liege) of the territories would have altered their status in favor of this.
The status of the Northern part (the Dutch Republic) was altered, by the legal owner (the King of Spain) in 1648, but did not rejoin the Holy Roman Empire in any way, whereas when the Southern part of the Low Countries (modern Belgium, the Austrian Netherlands) was inherited by the Austrian Habsburgs (who were also Holy Roman Emperors) in 1712 they chose to keep the exclusive status, because they would have only weakened their own position if they had altered it to its pre-1548/49 state.