LOL. I meant upper body push vs. upper body pull, just in case that wasn't totally clear, from what I actually posted.
And deadlifts are a special snowflake in lots of ways, anyhow.
As for balancing the program, OP, maybe consider 1-arm DB rows as another pretty awesome pull option? Also, chinups (yep, as well as pullups).
I'm in no position to be advising others how to set up their program though, so what lifts you keep (or add), and how you organise the lot... is up to you (or someone with more experience than me, maybe).
In case it's any use to you, my own approach to a lifting week right now is deadlifting and pressing once (on the middle day) and squatting plus benching twice (each side). Then other crap thrown in to balance, build muscle, and shore up severe weaknesses (e.g., hamstrings for me).