You've got a Smith machine. Don't be a closed-minded bro, use everything available:
Just to clarify, are those your current numbers? Or does "working up to" mean those are what you're aiming to get eventually?
Either way, you can learn to power clean in a few sessions, which means you can clean the bar before overhead presses. So, there's that.
That's not obvious.
I'm not sure how heavy the dumbbells go, but seriously, other than a rack, what more do you need to train upper body? You've got multiple bars, a full cable setup, at least a few dumbbells, a Smith machine, pull-up bar, preacher station, pec deck, ab bench, flat bench station, multiple free benches including an adjustable incline (which means you've got a decline bench if you toss a plate or the aerobic step under one side), and a Swiss ball (which can double as a "bench"/"incline bench").
Dude, if you can't train upper body, it's not the equipment's fault.
Seriously, you have way fewer limitations than you think. You should be able to make almost any program work in that situation.