If you are going to upgrade the driveline, go for something brushless, as it's not going to be any more expensive than a new brushed setup, but it will outperform any brushed setup by far.
The easy obvious choice would be to use the existing waterjets and just hook up new beefier motors to it.
The question is if the waterjets can take the strain of these new motors. I let you be the judge of that, I havent seen them..
The next question is your hull. What is it made of?
If its vacuum moulded ABS plastic, then don't waste any money on upgrading it. Sooner or later it will crack, you should just get a better hull.
If its a fiberglass hull, then it might be good.

You should also replace that lead acid battery while you are going at it.
A LiPo battery doesn't cost much, but it has way better energy density than a PB battery.

And for the transmitter question, how does this boat steer?
Does it have a rudder, or does it steer by putting differential thrust on the waterjets?
If its the latter, you will need a computer radio with a good array of mixing capability in order to run it as intended.