I don’t think tactical maps are too busy for this kind game and I don’t think tactical fights are very HoMM-like. Yes, strategic map is HoMM inspired to a degree, which is great, but there are not enough complexity there in terms of resources, creatures, etc., so strategic level feels very different and simplified. Tactical level is much richer though, in terms of options, destructible environment, so tactical maps need to be more complex than HoMM - the whole point here is to use destructible environment to help you win.
I adore this game and wanted to thank the OP for pointing it out. Don’t expect a HoMM clone, it’s very much its own game. And I find writing to be lighthearted and funny. :)