I've had essentially the same problem before, and was able to make it work for about a dozen batches with no trouble. It isn't ideal - the boil-off times were often in the three to four hour range - but I
was able to evaporate the water out over time. The only real problem I had was that I often had to use two separate boilers to speed up process, and that it made it hard to predict when to make hop additions (hence the reliance on First Wort Hopping in most of my recipes, which had the advantage of simplifying the process as well).
As it happens, I purchased a propane burner myself this weekend. Due to other issues, I haven't used it yet (I'd been planning a brew session yesterday, but didn't have everything set up for working outside until early afternoon, which was too late to get started). I expect that the burner will shave at least three hours off of my brew time, and working outside (as opposed to the cramped kitchen space) should make both the brewing and the clean-up easier.
BTW, if you are getting the propane burner, you would be well advised to spring for an inline water filter fitted for garden hose, as well as a garden hose specifically set aside for the inflow and a potable water hose for the outflow. From experience helping out at the Cover Hops Society's group brews, I can tell you that being able to run water outside rather than carrying it out makes things much, much easier. If you do get one, make sure it is a carbon block filter rather than a cheaper sediment filter model. I bought mine at Ace Hardware, and despite the fact that it wasn't designed for that purpose - it is an under-sink model that I needed to add a series of brass adapters to on each end to connect to the hoses - it works like a charm.
Amazon has several for sale, of varying quality, and
Midwestern Brewing Supplies sells a model that sounds very good. Make certain that the outflow hose is the white potable water (food grade) kind, or you may get off flavors.
