Ahhhh. I hate technicals!!
So sorry about your flat....that just plain sucks!!! I raced a TT with only a front brake once, and another time with handlebars that loosened when crossing some rough train tracks - but never one that stopped me totally. I would be disappointed too.
I race masters in the TT - and this year at states I raced masters road - but the "masters" categories all started together on the road - so we had all cats and a safe race. Otherwise - I would race open. Time of day for the race also influenced my decision as you mentioned earlier. Otherwise when we are road racing we are at the mercy of the organizer.
Personally - I might say race open in the TT next time if the increased competition may push you that extra percentage or two....
"Character cannot be developed in ease and quiet - only through experience of trial and suffering can the soul be strengthened, ambition inspired and success achieved" - Helen Keller