The power supply for your laptop should be labeled with the Watt rating for you to compare to the inverter you bought to see if it is big enough.
Also, regarding rental car insurance, American Express offers insurance for $25 (total, per rental, not per day) for I think up to 30 days or something. I had to check, but they provide up to $50k of secondary coverage, and $75k if a platinum card holder, which should cover your cliff roll.
My last company used National for business travel, and I never had a problem with them, and they had a decent vehicle selection. My new company uses Hertz, which has been alright so far too.