Tip 1: At the traffic lights, (and obviously stationary and with one foot on the ground) engage the front brake only and push foward on the handlebars to lift the rear wheel -- at the same time move the clipped in pedal to the 1 or 11 o'clock position. Ease back on the handlebars to let the rear tyre contact the ground again, and you're set to go.
Tip 2: Start looking at lower-tooth rare cogs to replace what you have now. I moved quite quickly from, IIRC, 19T to 18T to 17T with a 39T front ring. I am about ready to move to either a 42T ring or a 16T cog because I think my legs are ready for it. That will help with the fast pedalling downhill.
Tip 3: Don't overthink mounting and dismounting. I can't see it being any different to getting on and off a geared bike, frankly. But use Tip 1 to help get the pedal positioned to go.
Tip 4: Just ride -- you'll find after a while your body and mind don't have to pay attention (unless you change a lot between geared and fixed and find yourself attempting to coast -- which will be a very momentary lapse).
After doing my wedding century late in August with Machka on a geared bike but deliberately all the way only in a single speed, I can understand the SS attraction, too, especially on downhills.