Was the idea of a regency for Aegon VI and Rhaenys ever really explored by the rebel faction? Rhaegar may have been more agreeable to a surrender if he knew his children would succeed him, and it was possible for him to take the black. Or did Robert just really want the throne that badly?

No, the idea was not explored, because the Rebel Alliance acclaimed Robert as their king – note the order of operations there – and once you’ve crossed that particular Rubicon, there is no alternative to removing House Targaryen altogether.

And I should emphasize, because I’ve responded to a few of these, but the political logics of a lot of these alternate scenarios are not sound. Even if Rhaegar was willing to take the black (unlikely), and Rhaegar’s supporters would accept that (unlikely), it’s not a good idea for the Rebel Alliance to support a regency for Aegon VI, because infant kings grow up and have excellent motives to revenge themselves against the people who overthrew their fathers.