I don't see a problem with refilling the HLT during the mash because I don't think I'd want to have 170F water sitting around getting cold for the 60-90 mash anyway. Besides, you get your brewday moving along much quicker if you only heat up just over the amount you need for strike (6 gallons heats faster than 18). Now while you're mashing, start heating your sparge at a moderate pace so it hits temp at 60 minutes. I think it saves gas this way.
Wortmonger, I know your situation is a bit different in that you have a temp-holding HLT using electric and plenty of insulation but I still think heating the sparge during mash makes sense.