GERD is an issue near and dear to my heart, and I have been covering it a bit in my blog if you want to check the thoughts I have been having. I'll be posting a few updates in the next week!
I went off my PPI drugs (that I was on for a decade) about a week ago and have been supplementing with Betaine HCL to try to end my GERD. It has been an up and down process with a net up. I'll go more into detail about that in the next week or two on the blog.
I'm glad you're using hcl and pepsin; that's great stuff. Personally, exercising causes my esophagus to burn a bit, even if it has been fine all day. For example, a squat, by pushing down on your body, increases the internal pressure, causing stomach contents to slip up into our esophaguses, because they are weak. I just deal with it. I'm not going to stop exercising, and I suspect, over time, as I am better able to manage the disease with pepsin/hcl, my esophagus will become strong enough to keep this from happening. It sounds like you are also in the early stages of managing it with HCL and pepsin, so hopefully it'll improve for you too.
I'm honestly surprised by how closely your GERD seems to be related to exercise. I know when you exercise your body shuts down the nerves and machinery related to digestion a bit. Maybe yours just takes a long time to come back online. Eating before training is definitely a no for us, but it seems like you might have to avoid eating for a while after too. Personally, I switched from meat and sweet potatoes after exercise (while I deal with the GERD) to a protein shake with some hcl/pepsin, since it's easier to digest and get through the stomach quickly (pure whey). You might try that, or you might try simply fasting for an hour or two after exercise, while you make an effort to relax. I think Mark mentioned once that causes a growth hormone spurt or something like that.
Good luck with the gerd!!!