Running BBB on a cut?

I have been running BBB while bulking for about six months now. I’m quite happy with my progress, but I’m starting to get chunky and my pants are tight, so I think it’s time to cut!

I tried continuing to run BBB while in a 500 cal deficit, but I get absolutely exhausted after the main lift and even start to feel sick while trying accessories. Can’t seem to finish any of the workouts now. Are there any other programs that are particularly good for maintaining strength during a cut?

Thanks in advance!