I don't find doing a big beer a chore at all. I do lots of big beers (wee heavy, barleywine, old ale, belgian strong, etc.) and I find them no more a chore than a 5-6% beer. I do boil them an extra 30-60 minutes and it takes another 3 minutes to mill the extra grain. Sounds like you need to change your process and make some relatively minor changes to your equipment.
I batch sparge in a 52 quart rectangular cooler and boil in a 10 gallon pot. If you are using a smaller pot than that, you will indeed have issues with boiling enough wort. Also if you are using one of those cylindrical drink coolers you will be filling it to the brim and it will be the devil to try to stir.
By switching to a rectangular cooler you can do a thinner mash (around 1.5-1.7 qt/lb) which will be much easier to stir. This will be due to the thinner mash as well as having a shallower grain bed. Theoretically a fly sparge is more efficient. In actual practice, a batch sparge will give you the same or better results 95% of the time. On top of that, you will save over an hour of time on brew day by doing a batch sparge.
Lot's of folks here do batch sparging and will be glad to answer any questions about it. You should probably start by checking out Denny Conn's page at
http://hbd.org/cascade/dennybrew/ .
I hope this will get you started in figuring out the problem.
Wayne