Need 12v, 500mA for 10-12hrs- lightweight

So my clock capacity tester has shown me that I've got a lot more bad
batteries than good ones. So I'm in the market for some new NiMH
cells.

I was going to use my wealth of AAs to run a wireless headset on my
metal detector.

The wireless system was designed for a car [12v - or should I call it
13.6?]. All I can find for specs on it is that it is rated at
500milli-Amps. It is a Luxma transmitter that I bought on ebay.
Looks like the transmitter that goes with this set-
http://www.luxmt.com/pages/lhp888ht.asp
[the headset came from Newegg, is also part of that set- and Newegg no
longer has them]

I want the battery pack to be able to run it 10-12 hours- though it
isn't likely I'll ever be away from a charger for that long.

Weight is a concern as it is on a metal detector- and I'll be swinging
it with one arm for extended periods.

My first thought was to run it on 8 AAs. [I've wired it up and it
works on 8 [alkaline] AA's- but I don't know for how long] Then I
wondered if 10 or 11 would be better. . . . or a combination of 9v &
AA's. . . . or a single 12v. . . .

My lack of knowledge makes me ask--
*If* the 500mA is a constant, and I'm using 10 [to keep the math
easy] 2700mAh AA batteries to produce 12v- do I then have 27000
mAh's- and in theory could run the thing for 54 hours?
[if true, then I might go with alkalines instead of rechargeables- 50
hours is probably more than a couple months of use]

Thanks again-
Jim
.