Invading Iraq outright would have exceeded the UN mandate and risked alienating the United States Arab allies and at least have risked a protracted conflict which the administration was presumably keen to avoid. Given those conditions would Bush have ever been willing to take the risk of marching on to Baghdad? Creating the conditions for a successful 1991 rebellion seems more plausible than an outright invasion. But from a practical standpoint how would that happen? If you need to extend the Gulf War by another 48 hours how would that happen without a deliberate decision to overthrow Hussein? How do you put the Bush administration in a position where attack helicopters can be denied?
Religiously radicalized or not it's hard to see the Sunni population embracing what would have been almost inevitably a Shi'ite dominated government. Even in 1991 I think the ethnic/religious tensions in Iraq would lead to post Hussein tension.
Of course a lot would depend on just who would come to power in the aftermath of a successful 1991 uprising and how he would behave towards the Sunni population.
So assuming that the Coalition forces could inadvertently engineer the requisite conditions for a successful 1991 uprising what sort of person would rise to power after Saddam?
Certainly, intentionally trying to bring down Saddam would have exceeded the mandate. However, just extending the war 24-48 hours would have caused a lot more damage and greatly weakened the regime.
So, I think the best option might have been to continue the war for a day or so, advance toward Baghdad, but maybe not enter it proper except to destroy some bases there. US forces can work on managing 'optics' -- taking lots of prisoners, treating prisoners super well, giving supplies to people in areas the Iraqi troops are pushed out of, etc.
Yes, the coalition and/or UN might start calling for a termination of hostilities, but the US could stall and point to ongoing Iraqi violations (using helicopters to attack Iraqis who opposed him, etc) for at least a little while. After all, it was the US-led coalition that came up with the idea of stopping at 100 hours and that was largely because it was a nice, round number. They could have gone with 120 hours (5 days) instead without too much opposition.
In any case, with the additional damage done to the Iraqi military and other instruments of Saddam's power, he might have fallen after the allies left or, at least, had to spend years trying to re-solidify his control. If he fell after the hostilities, we could let the UN take the lead in managing the chaos afterwards.