I tried to review the four pages of feedback so apologies if I'm not adding anything new here.
I suspect a lot of the (non-bug) issues I'm experiencing with TB is because somehow Turn Based, with each character taking turns performing combat actions, got conflated with having DnD-like "combat turns" (or rounds), which just like in a lot of incarnations of DnD, last 6 seconds in PoE2. I suggest keeping the first part of turn based and getting rid of the notion of having turns/rounds, since this second aspect, more than anything else, changes the way stats and abilities work in such a dramatic way that the only thing that could be done is re-balance each stat or ability with this very artificial 6 second turn in mind.
Much has already been discussed about Dex/action speed, guns, AE-spell problems, shipmate AI issues, etc. But from what I can tell virtually every ability needs review to make sure they're still relevant in this new mode. For example, last night I looked at consecrated ground, a third level cleric spell. It recovers something like 5 health per round for 4 rounds. That's an incredibly mediocre heal for a third level spell, as it gets outclassed by the first level heal spell (heals base 30) and almost a second level spell that also does damage and has a longer AE range. Even with a super high intellect to extend duration, it still under-performs. In the regular mode, I recall it being a useful long term heal you can plonk on the ground and heal a decent amount of damage over time, partly because it ticks every 3 seconds rather than every 6 (per round). But in this new TB mode, there's basically no reason you would even select the spell, nevermind use it. That's just an example; there are lots of abilities that could use re-balancing to account for the dramatic changes that TB have brought.
Moving away from turns/rounds liberates you from having to arbitrarily decide something lasts 20 seconds -> 4 rounds (and thus re-balance everything radically). Instead, abilities last whatever they're balanced to last for, so Consecrated Ground could return to ticking every 3 seconds. Rather than listing character turn orders, you might additionally list when abilities are scheduled to be cast, activate, or expire (like those consecrated ground ticks). It would also help address the action speed issue, as a fast character would just go sooner/more often in the turn order than a slower, more heavily armored character. You could still keep initiative, as a factor for who goes first initially, but after that everything comes down to action speed which is modified by weapons, stats, abilities, etc. The fast rogue with a dagger might get 3 or 4 turns with regular attacks in the same time frame that a slower 2-hander character goes. This would provide a lot more strategic depth to weapon choice, stats, and abilities that is currently lacking in TB mode, which presently favors formerly slower, high damage weapons and heavy armor, and abilities that now are free actions. Instead, a free action ability--like an often used defensive spell like mirrored image--would return to taking .3 seconds to cast, then that character is back up for taking an action/turn provided no one else is scheduled to act sooner. If two characters are "tied" in the turn order based on them selecting actions that result in them being active at the same time, they can use initiative to break the tie.
TLDR: Ditch turns to avoid having to majorly rebalance all abilities and solve the current issues with stats and weapon balance. De-emphasize initiative except for initial turn orders and "ties". There's really no good reason I can come up with to impose artificial 6 second rounds for a computer game with mechanics where abilities, stats, and weapon speeds vary (for healthy strategic reasons!) in fractions of a second.