To add to my previous thoughts, there are pluses and minuses to the BCR and battery approach for the 5v ps2 design.
Advantages of using the BCR are that it will likely never have to be replaced, and that brings with it avoiding having to open your engines again... though if simply removing the shell and putting it back on causes things to break it sounds like there's some serious design flaw in there.
On the pluses for using a battery, some have reported issues with the charging circuit failing due to the repetitive high current draw of BCR-like devices. I'm not especially concerned about that one, but it is a thing. the main ones for me would be that a cheap NiMH rechargeable battery will last an easy 5 years and likely 10 or more years before needing to be replaced. at about 1/7th the cost of a BCR the battery is a much more economical choice, as the 50+years it would take to pay back the cost difference in using a BCR is likely getting into the point where the super caps could start to fail simply from age.
Over all, I'd say, if you don't care about what you're spending, go with the BCR. if you would rather save the money for something that actually provides some practical benefit to your layout, go with $3 NiMH LSD batteries.