halving the voltage will double the ah rating at 24V but you will still have the same watt hour rating and effective capacity, it will also have the effect of increasing the current through the cables hence the warming of the cables that you found, doubling up the batteries though will help reduce the overall sag and will reduce the Peukert effect, see wiki for an explanation of this.
The motor that you have will have an optimal efficiency rating at a certain speed, check with 4QD on that to find what it is, if you have current limiting on the controller I would use that feature and keep it at 48V but reduce the gearing to reduce the top end speed, this will give you more low down torque and make it more rideable on the throttle.
Throttle mapping may also help, again I dont know what the 4QD offers but other perm magnet motor controllers like the alltrax do let you adjust this so that you have a more even spread of power over the mechanical throw of the throttle, check with 4QD they are super helpful.
I dont blame you for trying out the lead acid option first, ideally and please dont think you have to change the bike a better motor would have been a brushless DC motor and a brushless controller such as the kelly controller, but you can make that an upgrade if you love riding the bike and think you will use it a lot, was going to ask if you have fitted a main contactor on the bike? its very important with a perm motor that you do, because if the motor controller fails there is a very real chance that the motor will run flat out until it hits something and stops, semi conductor fets almost always fail short circuit, this is less of an issue with a brushless controller motor combo but it very important with a perm mag motor combo that you have.
Lipo batteries would not sag any where near as much and would definitely improve the performance, they would give you more range as well partly due to the Peukert effect and their lower internal resistance.
The other thing that I was going to mention is the airflow over the motor and the controller, keep an eye on the temperature of both, mounting the motor and the controller inboard with no external airflow is hard on both, keep an eye on them and utilise motor and controller thermal overload protection if possible.
Speak to Steve at Jozztek about the batteries, in theory you could run a lipo pack in parallel with the lead batteries at the same voltage although you must not charge them that way, it would be best to just run lipo, however for now have some fun on the bike with the lead and think about lipo in the meantime.
You could buy 4 high capacity lipo pack from hobbyking and just try your own 10AH pack and see the difference, I think you would be amazed.
Newbie way of doing it it buy a 4 channel charger, you can charge all 4 packs in 1 go, each cell is monitored whilst charging and balanced, check the hobbyking site for the details.
4 of these
http://www.hobbyking.co.uk/hobbyking/st ... duct=19156
and one of these to charge them
http://www.hobbyking.co.uk/hobbyking/st ... arger.html
You would also need a good DC power supply to run the charger like this
http://www.moonraker.eu/alinco-dm-330mw ... wer-supply
I have been running this combo on my ebikes for 5 years now with no problems, your bike is a bit more demanding on the power front so you would have to use more expensive batteries, you would also need to watch the power used as well, I would suggest using a high current cycle analyst as you dont want to run the lipos down low below 3.2V per cell.
right its late im to bed, would love to see some video of the bike running