Core strength is king. It gives your legs a stable platform to pedal against. Without it, you will tense your shoulders up to counteract the rocking about.
I have to remind myself to relax onto the bars now and again. I start to tense up and feel achy so have to give myself a reminder to keep my upper body relaxed.
I also get the issue with glasses - my helmet slips down, pushing my glasses down and causing the top of the glasses to get into my line of sight. I might try tightening my hat, otherwise I will attempt to buy myself out of the problem.
Exercises I like to do for core stability and to help with bike position:
Crunches on a swiss ball - either normal sit-ups or starting in a press-up position with thighs resting on the ball, then crunch until your ankles are on the ball and you are in a ball shape. Don't fall off.
Also, with kneeling with fore-arms on the ball, in TT position. Then roll your arms out to stress your core, delts, lats etc.
Something else I am convinced helped me was doing the Tour of Sufferlandria on the TT bike. So, a good number of hours in TT position, but also I was following the instructions perfectly: you have to do a fair amount of high cadence stuff. Before starting the Tour I'd have struggled to hit 120rpm without bouncing in my seat: by the end of the tour, I crossed the finish line in top gear at an indicated 83kph, 570W and
152rpm.
I think I really improved my pedalling technique, which translates into less rocking and less need to attempt to stabilise using my shoulders. I totalled about 100km on the TT bike this weekend and the main feeling I have is that my hamstrings are aching more than my quads. Surely a sign that I'm learning to pedal in circles?
Technique? On a bike? Who'd have thunk it?