Intermediate programming with golfer's elbow

Some background in case it matters:
I am on my second iteration of The Bridge 1.0, about to start week 4. Weigh about 200 and trying to slowly cut weight. Current e1rms in squat/bench/DL are 375/290/450.

My problem:
I’ve started to experience some golfer’s elbow. It got particularly aggravated by pull-ups with a ~50% supinated grip in a crappy hotel gym. I have been feeling a bit of pain while benching for a while though, and now it also hurts to do rows.

Would you recommend that I (and more generally people feeling some elbow tendonitis) keep doing The Bridge with the same exercises, The Bridge with some neutral-grip exercises thrown in, or switch program? I am thinking of doing neutral-grip dumbbell bench press instead of close-grip bench and maybe neutral-grip bench press (I have access to a mixed-grip bar). I will also try neutral-grip pull-ups.

Are any of your other intermediate programs better suited for dealing with this? I was planning to do your hypertrophy 3-days-a-week program after The Bridge.

Thanks!

Thanks for the post. How are you managing since the OP? Typically, I recommend adjusting loading before adjusting exercises. Have you tried manipulating load?

Still some pain. It got a little better, but it gives a stinging feeling when I unrack in bench press, and hurts a fair bit when doing e.g. rows. I am able to do overhand chin-ups just fine on the other hand.

I have not tried manipulating load. To be honest I wouldn’t really know where to start on that. Just decreased load?