I don't know how, and I don't know why, but as far as I can tell Golyak becomes unkillable using the Firefly method with either the Free-For-All Pack or the Getting Busy Bonus Pack (and I'm going to assume this is the same for having the Four-Play Pack installed). This happened on the Xbox One S with an Xbox 360 disc, in case that's relevant.
For reference, I'm referring to this method:
The tactic is to hit him with the first Firefly shot so he falls, and then he can be killed on his way down with more shots. This only works if he stays by the edge (i.e. he doesn't run away).
Older NG+ attempts I still have on my hard drive had 20 shots at Golyak (where he never ran), and 13 times he fell (65%) so he had a chance of dying. The amount of times he ran away with any of the DLC installed was 25/25. Not a big sample size but I'm not willing to try even further hoping it's just a long fluke.
So unless another strategy works faster for him, NG+ and his Time Trial needs to be done without DLC for the best strategies as far as I can tell. This also rules out using the Racecar instead of the Supercar for Sovetnik/Romanova, which would've been ~3.5-4.5s time saved while Firefly Golyak is ~6s faster than Shotgun Golyak (without factoring in swimming over Rabotnikov to make it even faster).
If anyone can confirm or deny they're experiencing the same thing, that would be appreciated.