JoeN:
I ran for a good 5 minutes prior to fireworks. Can a backwards cap survive that long before igniting?
Yes. When reverse biased, a value-metal cap actually breaks the oxide down. Until the oxide is thin enough to cause a short, it won't break down.
JoeN:
Everyone says no Tantalum on power supplies
There is a big difference between Tantalum-MnO2 and Tantalum-Polymer. Polymers are actually preferred for power supplies... Switching power supplies...
A 7805 isn't sensitive to ESR since it is a linear supply. In fact, 10uF is well beyond what most manufactures recommend anyway. You could easily get away with ceramics or aluminum Electrolytics, and they'll be cheaper.