I think you need to get this solved before you go back to riding 100+ miles a week. I know you are persistent and I'm confident you'll get it figured out.
Here are my suggestions:
Straddle the bike. Put your dominant foot in the DOWN position on the pedal. Use your other foot to push yourself a long like a scooter. That might get you more comfortable with that starting sequence.
Do the same thing, only this time your dominant foot in a HALF-UP position (so that you don't go too fast), and instead of using your other foot to push you along, use the 1/4 pedal stroke to push. In other words go from the half-up position to the down position but no further. Since you have clips you can immediately get the pedal back into the half-up position for the next push. Keep your other foot down, lifting it just enough to move along a little.
I think someone else mentioned practicing standing on the pedals while you're riding. That might be challenging at your comfort level and ability but give it a try.
I saw someone do an unusual bike mount, which looks more difficult to me, but maybe it's natural to some people. He did NOT straddle the bike, but put his one foot on the pedal, pushed down and in one smooth motion while he was moving, he swung his other leg up and over the seat.
You said you know you're supposed to start off in a high enough gear to get some momentum. Try a lower gear. It'll start you off slower.
Good luck! I know you'll find something that works!
2009 Trek 7.2FX WSD, brooks Champion Flyer S, commuter bike