Yea, if you have a cheapo battery giving you problems, ultracapacitors will probably fix the issue. You bought hybrid ultracapacitors which are like halfway between a capacitor and a battery, so yes the internal resistance is higher, but you also have some current available from the battery to help it out, so it may work.
I've heard of quite a number of people complaining about BMS equipped batteries doing weird things to their cars, and my own lithium ion battery is also acting up, so I also bought a small ultracapacitor pack in hopes that it would make all the electrical issues go away. It's so small there's no appreciable self-discharge current, it can only help in starting the motor, and it weighs 100 grams so it can't really hurt.
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