Is it possible for there to be a successful Warsaw Uprising in a recognizable WW2, with the large majority of the fighting force being the Polish Underground Army?
Some problems were (at least to my knowledge) some mistakes in coordination in the rising leading to some of the surprise being lost and also a large lack of weaponry. The lack of weapons where mostly due to the Germans raiding a few warehouses and underground factories in the months leading to the rising. This was due to the high command getting scared of some of the stockpiles being found and so they scattered them into the countryside, where ironically many where found. (I think, I'm no expert)
So, if you could stop this, then you have a better armed AK. Then, you need to try and get the groups better organized and informed. That would lead to less fubars.
However, the main problem is Stalin and the soviets. In OTL Stalin waited for the rising to be crushed before advancing to get rid of what would have been the main opposition to a communist Polish government. So, he naturally also did not many allied supply drops, as they would have to land in Soviet territory to then refuel and fly back to England or Italy. So if you can fix this problem, then you can have a successful rising. However, if you remove the problem of a uncooperative Soviet Union, then the reason for the uprising is mute, as its main goal was to set up a recognizable Polish government before Stalin set up a puppet, and any cooperative Soviet government wouldn't have plans to set up a puppet, IMO.