The problem I have with push presses is how much wider a grip I'd have to take to do them. To accommodate the length of my arm segments in a clean I have to take a grip basically as wide as my bench press on the bar. Even then, the thing is still pretty close to the neck.
That’s understandable, with my proportions I don’t need to widen my grip too much to get it to rest on my shoulders so it works pretty well. Can be a bit rough on the knees though if you’re not careful.
I think I’d stick to close grip or LTE in your case or even look at one of Andy Baker’s power building programs and see how he programs for a little additional arm work. Lots of free workouts he puts up on his blog. Have you tried close grips for heavy triples before?