Push-press tends to emphasize upper body more than lower, although it does serve as a speed and strength assistance exercise for the jerk.
Deadlift from floor or Romanian DL starting from top
Clean and variations (if you have a coach to make sure your tech is good)
Snatch and variations (ditto)
Also, you might try the front and back split squat. This is basically a lunge, except you don't push off the lead foot and come all the way back to standing with feet together after each rep; you just push back to the point where you're in a split jerk stance and you're completely stable, and then step forward to do the next rep. I recommend the front and back split squat because your leverage may very well be better in this exercise than in a full back squat, since you're so tall. I'm also fairly tall (6'), and I have long legs, so I can split squat more than I back squat. More load----> More strength.
The split squat emphasizes the back and front of the leg more or less evenly, so even though it is technically a 'push,' it, like the powerlifting back squat, sort of overlaps both categories.
The oly lifts are great, but since your overall strength is still quite low, I doubt whether you need to do any specific power/ speed work. Just work strength on the one hand and running on the other, and you'll get what you need.