Nigers are usually reef safe but they grow HUGE!
Not all trigers are fish only however. BLuethroats and pink tails.. eventhe Sargassum triger are reef safe.
Mixing tangs... well i have managed it.. 3 emperors and an orange shoulder. before this i had a sohal. Yes there was a bit of bullying and jostling.. at times it even seems seemed quite frightening but within 3 days they were swimming happily together and now form a lovely shoal.
You could try a few things should you be worried.
Place a mirror on the side to distract the regal tang.
Move all the rocks around and give the regal no territory it rcognises to fight over.
remove the tang and allow the new tang a few days to settle in first.
I will add lastly that tangs wont solves the problem you are facing, tey are merely stopping it being a nusance. therefore you will still have high nutrients as you have no cleanup crew. The trigger you have sadly seems to be effecting the balance of your system and i urge you to rethink its long term habitation of your tank.