Probably way overkill, try doing both of these resets 2-3 times each. Intel iMac SMC and PRAM resets
The only solution I can think of would be to create a boot disk. Is this even possible?
I keep an older wired USB keyboard for just those instances; using a wireless keyboard with any startup command is tricky - during a service call with Apple, mine would not work so, after 4 tries, I pulled out my old keyboard and was able to do what the Applecare rep wanted me to do.