[nativepaul]

You are perfectly correct for the first part a 4s 4AH pack has the same energy as a 6s 2.7AH and your battery will weigh the same, so if you gear you 7XL way down you will get the same input power, and maybe more power out due to greater efficiency at lower amp draws, however your motor will be spining half as fast again, 45k instead of 30k on 4s and this may lose you some of the efficiency that you just gained. It would be better to fit a 10xl instead of the 7xl on the original gearing, to spin the same 30k rpm, the 10xl has its max efficiency at lower currents than the 7xl so its you lose none of the efficiency that you gained with higher volts.

The second benefit isn't realy there, if you where to carry on using 4AH packs in 6s you could use 15c instead of 20c, but your battery would weigh half as much again as the 4s pack.
If you use a 2.7AH 6s pack like you sugested to keep the weight the same, you will be pulling less amps but have smaller cells to pull it from so it is still the same 20c rate.

If you want to use cheaper lower C cells you will have to install larger cells which isnt much cheaper per AMP you need, but is alot cheaper per AH capacity, but you will pay for it with weight, for example (using made up prices) a flightpower evo20 6s 2500mah costs around £100 and weighs 400g
a cheaper lower C lipo would have to have 4000mah to handle the same amps and a cheap 4AH pack will likely cost the same £100 as the evo 2.5AH, that seems like an extra 1500mah worth of runtime for free, however nothing is free, it's just that you don't pay with cash you pay with weight instead by hauling another 200g of battery around with you.

lol you got loads of replys while I was writeing this, I type too slow.