I don't know how much chin ups actually drive presses to be honest. I press a lot, but I'm mediocre at chins. If you want to get better just do 1x/week weighted. Maybe cycling between sets of 2-3 and sets of 5-6. And then another day of the week doing BW for reps. For the heavy weighted day we almost always do chin ups. For the BW day we do alterations between chins and pull ups. I've been doing this with my swimmers for years. Works pretty good for most