You might want to have a look at my (unfortunately unfinished) TL
A Different Chalice.
To put the answers to your OP questions developed in that TL in a nutshell:
One possible divergence contributing to greater radical Hussite success than OTL (which is really a tall order since their success was astounding anyway), and the one which I chose in that timeline, could be to have the moderates dominate in Prague in 1419-21 or maybe even later, leading to the coronation of a Hussite Bohemian King, who is overthrown by radicals later. A moderate stage followed by a radical stage is the revolution model of France 1789 or Russia 1917, both arguably revolutions with long-lasting legacies. The Hussite revolution was, at least in the capital, quite radical in 1419-21 until the radicals discredited themselves, after which Prague remained firmly in the hands of the so-called "moderates" IOTL. Turn the sequence around (in my TL by having Jan Želivský assassinated), and Praguers get a better chance to become convinced that merely electing a King who speaks (some) Czech and being allowed to sip wine in church isn't going to change their lives as much as some of them may have wanted.
As to where all this could lead... well, I had it interact with conciliarism, with guild and peasant revolts elsewhere, with the Strigolniki in the Orthodox realms, with the Lithuanian war of succession etc. I did go for the Hussites pulling a Switzerland, though to be honest, it probably wasn't a fulfillment of the OP condition insofar as I didn't have Taborites, Orebites etc. utterly defeat their aristocratic rivals but rather relegate them to a less relevant position withn the new confederal Hussite polity.
Once the Reformation gets started in earnest, there's probably going to be a lot of social conflict. Perhaps it becomes eerily similar to Capitalism vs Communism in our world...
I agree that social conflict is really at the centre of this.
What kind of government would be under Tabor and their leader Prokop the Great? Their plans for hussite state where rather vauge.
So you're sure you want Prokop Holy rise as Tabor's leader? That might imply a somewhat later PoD than what I proposed. Either way, the purges of (to use Soviet terminology) left-deviationists (Martin Huska et al.) and extreme millenarianists had happened already, and Tabor, Pisek, Louny, Oreb had become militarised communes not unlike those of the Old Swiss Confederacy. Really, looking at Swiss history gives you a lot of hints - in those days, people weren't thinking in terms of "what kind of constitution will our state have?" yet; both "constitution" and "state" would be slightly alien concepts to them, and even "our" might not denote what it does today in the context of that phrase. Sooner or later, a successful radical Hussite polity will have to include Prague, and when that happens, Prague automatically becomes its centre, although Tabor et al. might retain an important status, too. How to balance the very different powers of such communes is one key question to be answered; the other question is that of social order and the military. For both questions, Switzerland might provide a good indication again: with regards to the first, a consensus or near-consensus principle is going to be likely formally, which means dissenters are going to have to be brought in line through negotiations and brute force thinly veiled by some legal justification, for "proportional democratic representation" or something of the like is simply anachronistic. With regards to the latter, it is likely to have different sorts of "cantons" (I preferred the Czech term "obce" because obec, like Russian obshchina, also carries connotations of communal ownership etc.), some of which are more traditionally organised (with markets and guilds and accepting of the existence of a Bohemian nobility as a separate social order) while others show varying degrees of egalitarianism (which would almost certainly only include (the locally accepted flavour of) male Hussite believers who are considered permanent residents because they have some land or house allotted to them in the obec and who take up military (reserve) duty).