Personally I wouldn't spend more than 2 hours doing the circuit, you won't need long in AA for starters. As for which lounge is best, that's a very common question here:

http://www.flyertalk.com/forum/briti...ld-lounge.html
http://www.flyertalk.com/forum/briti...e-hopping.html
http://www.flyertalk.com/forum/briti...e-lounges.html
http://www.flyertalk.com/forum/briti...ge-advice.html
http://www.flyertalk.com/forum/briti...minal-3-a.html
http://www.flyertalk.com/forum/briti...ld-lounge.html
http://www.flyertalk.com/forum/briti...st-lounge.html
http://www.flyertalk.com/forum/briti...ptions-t3.html
http://www.flyertalk.com/forum/briti...l#post22586399
http://www.flyertalk.com/forum/briti...ch-lounge.html
http://www.flyertalk.com/forum/briti...lounge-t3.html
http://www.flyertalk.com/forum/briti...e-lounges.html

In terms of rechecking bags you have already collected: If you have status (or travelling Club or First) yes you can do this before going to London, but it has to be done at T3 if (I assume) you collected it at T5. Normally there's a 3 hour rule for longhaul, 2 hours for shorthaul, but your shiny card gets you out of that restriction.