HI Derek
Yes I fully understand. The LiPo will certainly improve your speed. I moved to brushless and LiPos with my fast boats but LiPos work well with brushed motors. There is so much more power available and provided you follow the guidelines re charging and discharge cut off they are OK. You may need to fit a warning device to the boat to prevent over discharge of the LiPo but they are cheap and will save your battery (and boat).
Your motor will get much hotter so you may need to consider water cooling. My speed 600s in a small Perkassa were OK on NiMhs but started cooking on LiPos. The 700BB Turbo are a much better motor and should really develop lots of power at 11.1v Hopefully your ESC will handle the fully charged voltage and higher current.
Dave 😀

HI Dave
I acquired a Billings Palm Beach jet boat from around the late 90's with a 9.6v 700BB turbo. Was on 8.4v, I put 12v in, much better. I was told that this jet & motor unit runs well on 14.4v. So as its a mans thing for MORE POWER, I fancied trying it. I do have a brand new spare motor laid around if needed. I'll just bide my time until I stumble across one. G oing to give a 3 cell Lipo a go to see what happens (less weight). Just need it to stop raining on club sailing days 😀

HI Derek
I have a similar background with electronics and have also built several Electronize. I noted your comment re cost and agree the Mtronik are costly so did not mention their offering.
I am assuming the 8.4v is not providing enough power hence the need for the higher voltage. if the model has a motor that is also 15 years old it could be past its best performance wise. if you have another motor you could try replacing. if the new motor runs on a lower voltage this may be an alternative and even if you have to buy a motor it would be cheaper than the ESC.
Good hunting
Dave

There is absolutely no info on the ESC, it does have reverse. I use 8.4v currently on it. Used electronize for years, those with the relay, Used to build them up for others just for fun when my eyes were younger. Best thing I did with those was to install a socket for the relay as they were a common failure. Still have several in use. The only ones on ebay over 12v without water cooling have a fan or have a hill hold for trucks and for 2 motors. Mtroniks do one, but hate paying their prices.

HI Derek
Not a lot to see. is there any detail on the other side of the controller? Judging by the wires it is a fairly high current ESC. Early ESCs were usually aimed at the car racers and did not have reverse. Can you reverse yours? 7.2 v NiCad/NiMh were common and ESC's were rated up to 12v.
To use 14.4 you will need a more modern ESC that will be capable of handling the higher voltage. Electronize are good to 24v but you will find others if you search the web.
As the unit is sealed it is not possible to see what power FETs have been used. Unfortunately if you exceed the Max voltage they will be destroyed so unless someone can identify your ESC you cannot be sure.