I would love to be able to play this game in single player and simultaneous turns! :D Is it possible?
This is not possible.
Heroes of Might and Magic has always been turn-based, which is very distinctive from real-time strategy games like the Warcraft and Starcraft series. You can't expect the software to support such a change, though with some modifications it could probably work from a game rules perspective.
There is little reason to do this
While simultaneous turns (STs) are possible in HotA, a mod for HoMM 3, the limitations placed upon that mechanic make it totally irrelevant for playing against a computer opponent. Basically, if you interact with each other or the same object, STs stop, and Blue players' turn is canceled and has to be replayed. With or without STs, there is not supposed to be any change in actual game results: you only save time.
Also, there isn't much benefit to this. When human players take large amounts of time for each of their turns, waiting for your opponent can be tedious, boring, and frustrating.This is why you need STs in the first place. After you meet for the first time and STs stop, the game is likely to be over soon, so you avoid most of the wait.
At the same time, a computer opponent doesn't take anywhere as long as a human to finish their turn. This is why you don't need STs against a computer opponent in the first place, as it would result in practically no changes.