The origins of the ossuary or charnel house (carnarium) in medieval burial practice are obscure, but we have references to its use as early as the twelfth century. Beginning during the Carolingian Reforms and intensifying over the course of the tenth century there was an increasing insistence that all Christians be buried within consecrated ground. This trend parallels the formulation of a more standardized death liturgy and a weakening of prohibitions against tomb violation. Demand for burial in sacred space, of course, meant a limited number of graves were available for use at any given time. Reburial as a rule became increasingly more common and as old graves were opened for reuse, their occupants were removed to make space for the recently deceased, and the remains placed in a charnel house. The use of the ossuary, then, preserves this insistence on burial within sacred space. The concern of the practice was not so much over whether or not the body is intact, but whether or not it was protected against malevolent forces that lurked outside the confines of sacred space. Thirteenth century councils in Germany even went so far as to require churches to provide ossuaries in burial grounds!

Now that is not to say there wasn't tension over the division and partition of human remains. As odd as it sounds, the practice was both acceptable and fraught with controversy, as people were indeed anxious about the threat to the integrity of the self caused even by the natural decay of the body in the grave. However, the ossuary can be seen as a bulwark against the fragmentation and scattering of human remains, gathering them together in one consecrated area and offering the protection of a communal and sacred space. Medieval theologians of the twelfth century expressed confidence that God would restore and reassemble the dust and bones of all Christians, ensuring an ultimate victory over partition and decay. Even within ossuaries, identity could be maintained; skulls were sometimes labeled with the names of their owners and important individuals might be set apart and given preferential status within the charnel house. All of this does not mean anxieties with regards to the practice disappeared entirely, but confidence in the restorative nature of resurrection and the overriding concern of burial within sacred space ultimately created space for such practices to take root.

So in that sense I am a bit suspicious of your tour guide's explanation. I admittedly know less about 16th century Italy, but I am not aware of any teachings of the medieval Catholic Church that required a skull and two bones for resurrection. Did they elaborate on where their information came from?

I can only answer a sliver of your question.

This has gotten me thinking about the Catholic tradition against cremation

Historically, the Catholic Church was against cremation. It was banned fairly early on and that continued through the 1917 Code of Canon Law. The 1983 version of the Code of Canon Law does not have such a ban in place. It states in No. 1176, 3:

§3 The Church earnestly recommends that the pious custom of burial be retained; but it does not forbid cremation, unless this is chosen for reasons which are contrary to christian teaching.

That Canon is in force currently, and it means that cremation is permissible depending on the intent of the people choosing it.

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The rest of your question is interesting, but I cannot answer it.

You could try asking at /r/Catholicism as well (with the understanding that you'd be asking a Catholic forum, and that sources are not required over there).