The program you linked to doesn't call for "ridiculously heavy weights" on the strength day. It works up to a heavy set of 3-6 not to failure. If your shoulder can't handle that, then you should probably consider spending a month or so prioritizing shoulder health, not chest size.
But like dagill said, that program would deliver everything you need if you follow it as-is. Almost every single "chest specialization" program uses at least one heavy day plus at least one lighter day, because that's a very effective way to focus on a bodypart.
The only other option you might consider is using some general tweaks to improve your current chest training, instead of a full-out chest specialization: https://www.t-nation.com/training/best-chest-training-tips-period