as someone who has dealt with vintage electronics you most likely have to replace every single capacitor as there is a good chance a few if not most probably dried out.
Seeing you changed a few out, but aren't sure if you got the values right that could cause a lot of issues for example if it uses a tank circuit for tuning where the cap value can drastically change the frequency it will receive. Even if you didn't change them out the caps drying out could cause the capacitance to change, and cause issues too.

as for the ESP cam losing bluetooth connection. I can only take 2 guesses first guess is the motor is causing interference with the BT radio signal. Best bet IMO would be put the antenna in the front as far from the motor as possible.

Another guess is it is a possibility if you are using AA's (it looks like you are using the original battery compartment) the batteries voltage might be dropping low and causing it to lose power in blips.

honestly easiest option IMO (especially if you happen to own a 3d printer just guessing by having esp's lying around ) just buy a cheap brushed 80a ESC(it could probably be 40a I just like being safe in these things), a cheap servo, and a cheap radio, and mod it. Most expensive part will be the radio which looking cheapest I see are $30 usd... I remember when they used to be $15 >.> total cost would be like $60 usd if you go cheapest.
Only real modification needed to be made would be to make a servo mount for the steering.