Well, as this is under an actively used Catholic cathedral, and Catholics typically like to do our services on top of our saints, I imagine the clergy and the diocese has something to say as to how the bodies are treated.
However, most churches don't have full bodies anymore, for obvious reasons. However, when the altar is stripped (for example on Good Friday). If you were invited into the sanctuary... you would be able to see a stone, on which there is inscribed several crosses. Under each cross is a relic, set into the stone. The priest consecrates bread / wine over the stone.
In terms of provenance... you can't sell a relic, but most monasteries, shrines, the Vatican, or other places that have burial records, will provide relics upon request, if available. Orders keep careful details of their martyrs and saints. So for example, a Dominican parish will often ask a Dominican priory with burials of a Dominican saint for a relic. We have indeed even entered the modern age where some monasteries / priories / convents even let priests request relics online!