Ric, there are MANY discussions of anchoring techniques if you search around the interwebs. I suggest you do a bit of reading up on anchoring techniques, and then think about what you're attempting. It is quite possible to set an anchor out, then tie off to land, but before doing that, you need to consider ramifications, such as a change in wind, current, etc. I'm guessing that with the falling lake levels, you will anchor off your dock to get to deeper water, and can't actually use the dock.
A 272 dang well ought to have a masthead all around white light for anchoring. Don't you have a house battery? Colregs say you need an all around white light visible at 1 mile for anchoring. This requirement can be met by a kerosene lantern, even. Many folks use a battery powered LED lantern, hung about 1/3 up the mast by the main halyard. Instead of burning through AA batteries with a lantern, you might consider one of these Davis Mega-Light Utility lights, hoisted up the main halyard, plugged in to the house battery. I believe they are now LED, at least, the ones I saw at the boat show recently were LED, so you get low power draw. The photo cell to turn on and off is a very nice feature. The old days of the Bebi Owl anchor light are gone, now that Bebi has closed up shop. The Davis is the closest thing I've seen recently. Of course, this all presumes your masthead all around is not working, and that, if it is, it's an incandescent that draws more power than LED.
I wouldn't run A/C mains from the dock to the boat. That just sounds like a recipe for disaster. Nor would I keep a battery on the dock - there's plenty of room for a house battery on a 272...
Hope this helps some…
Brian