this probably won't help your situation any, but this is what i did on my most recent batch. i just recently got a 7.5 gallon pot and now have two brewpots also (the 7.5 and a 5 gallon).
also, like you, i have limited choice on my brewing options. i brew on my elec. stove. two batches ago, i got the 7.5 gallon pot so i could attempt full boils. the electric burner struggled to get anything more than a rolling boil.
the last time i brewed, i used both pots. i steeped my grains in 3 gallons of 155* water while boiling 2 gallons in the other pot. once steeped, i added my extract to the 3 gallons, stirred it up well, added the 2 (now boiling temp) gallons, stirred, added hops and boiled for an hour.
doing it this way allowed for a little more vigorous a boil. i haven't been able to taste either batch yet as they both are still in carboys. of course, with a 5 gallon pot, i wouldn't recommend doing this, but maybe on a smaller scale? or if you could get a larger brewpot you could try it?