I initially tried the Verizon kickstand case with the extended battery, and it didn't fit (not snug enough). However, I just read in another forum that someone was able to fit the kickstand case on the back by removing the back cover first.
I can confirm that with the extended battery and no back cover on the phone, the Verizon kickstand case fits perfectly. I don't have any major concerns leaving the back cover off with the case on since it covers everything just fine. The only minor concern is when you extend the kickstand, it does expose just a bit of the internals to the air.
FYI - I even tried placing the stock back cover over the extended battery (which doesn't fit very well), and the Verizon kickstand case still did not fit snugly over top of it.
This is the case that I'm referring to:
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