Appreciate all the good ideas here, guys. I did some testing with all of your suggestions and also tried a few other things that I was curious about. This is on a hired adventurer cheated up to level 20 if that makes any difference.
Works with Forbidden Fist ability
Turning Wheel
Tuotilo's Palm
Helm of the White Void
Kahako Nihi
Lover's Embrace
Does NOT work with Forbidden Fist ability
Swift Flurry / Lightning Strikes
Heartbeat Drumming
Hylea's Talons
Two Weapon Style
One Handed Style (?)
Reminder that this is with the vanilla game of course. Some of these findings like Helm of the White Void giving accuracy to affliction attacks and being able to get Frenzy from Lover's Embrace just by having it equipped while using other abilities are probably already known or apparent, but I figure I'd mention it here as confirmation that it still works with the vanilla Forbidden Fist ability. What's interesting is that the other gear enchantments that work with Forbidden Fist (or at least the ones that I experimented with, which are Precision Striker on Tuotilo's Palm and Always Armed + Overwhelming Assault on Kahako Nihi) are specifically said to be applicable to unarmed attacks. So Forbidden Fist might be coded as an unarmed attack but not a weapon attack, which possibly explains why it interacts with these item enchantments but not weapon attack abilities like HBD or items like Hylea's Talons, but I'm not sure if that's an actual or relevant distinction in the code. What's really confusing though is that Forbidden Fist will get the burn lash from Turning Wheel but not the shock lash from Lightning Strikes. Really not sure what's going on there.
Another thing I tried testing is Two Weapon Style, which I believe doesn't have any effect on Forbidden Fist. I tested it before and after taking the ability and didn't see a difference in the recovery time. I tried this with two fists, two plain daggers, fist with Tuotilo's Palm offhand, and a plain dagger with Tuotilo's Palm offhand. For curiosity's sake, I then respecced and took One Handed Style and equipped a single dagger to see if that would have an effect on Forbidden Fist, which it doesn't as far as I could tell. I didn't see the added accuracy you would normally get from single wielding get applied to Forbidden Fist nor did I notice any hit to crit conversions, though I admit the testing might not have been extensive enough. I didn't test Two Handed Style, either. I'm thinking that Forbidden Fist is just it's own thing and none of the styles apply to it, but this might bear more testing and corroboration by others.
Some other miscellaneous testing. 1) The proficiency modal for dagger and quarterstaff does indeed work the way you've both said it would, so you can get all of the benefits for free while bypassing the negatives by spamming Forbidden Fist, which is a really great idea for this build and particular play style. The small shield modal, however, doesn't work; it looks like you don't get the extra accuracy after blocking an attack if you then use Forbidden Fist, unfortunately. 2) Dance of Death will not get cancelled by the self damage you take from Forbidden Curse. 3) Crucible of Suffering and Rooting Pain seems quite strong with Forbidden Fist spam as mentioned, giving you a practically constant defense bonus and regular interrupts in an AoE. I got Forbidden Curse down to 2.8 seconds with this test character, but I'm sure you could generate wounds and these effects at an even faster rate with some more optimization.