Any noticeable upgrade options for the cheap 1500w rear hub kits?

My first build is a Specialized SX Trail that I installed a Craigslist special 1500 watt rear hub kit - the bare bones kit with just three LEDs on the throttle. It came with a cheap Chinese 48v 14ah downtube battery. I'm really enjoying it! But, like most of you I assume, I soon began to wonder if more power was easily obtainable? From my reading it sounds like the rear hub motor can take more than its being given. Getting a controller that puts out more amps would do no good by itself I assume as my cheap battery probably only puts out 20-25amps continuous, is that correct? So, to increase acceleration/steep hill climbing/top speed I would need to upgrade the controller AND the battery.
Again, I'm happy with it as is, but just trying to educate myself as to what is possible and how much it would cost. Can you guys tell me what you have done to upgrade or suggest what you would do? A 35-40amp controller and a battery that would put out that amount continuous? I think I've read that sustained hill climbs/etc might overheat/damage the motor and I would only use those levels for short bursts - I'm pretty easy on my equipment.

Thanks in advance.

A truly good quality bigger battery can cost more than the total so far

But totally worth it, in fact long term becomes required and more economical on an amortized basis.

Get a controller compatible with CAv3 and it will derate amps/power when the motor starts overheating.

Build everything so you can eventually upgrade the motor too -)

Thanks for the reply.

Can you recommend a controller and battery? Maybe one on the lower end of the price spectrum that would accomplish my goals and one in the middle of the spectrum?

Thanks again!