I am working right now on replacing the EUC batteries with RC lipo. The answer to your question is yes. You can make your own battery for an EUC, or have one made for your requirements. The BMS is the main problem, for most recent EUCs controllers are designed to receive the BMS data and manage them in the security loop of the firmware. Ideally, you will build your new battery with the original BMS and assure the same connections to the controller. You can use any cells, only I would recommend to avoid cells that have lower specs. The controller will pull the current that the original battery was capable of, and interpret the failure to supply as a low capacity, thus will trigger safety warnings: tilt back and beeps, then cutout.
So you need equal or superior cells to rebuild your battery. Most EUC of the last 4 years are built with Samsung 21700 cells, usually the 50e or 50s. They are common and easy to source. If you have the budget for better, I recommend Molicel P50b, that have a much higher C rate (the Samsung 50s can supply 35A peak, while the Molicel 50b can supply 60A and last longer).
If your EUC is older, your battery might be just worn out (too many cycles). If it is recent, it is possible that it is still good, only discharged lower than the controller firmware accepts to charge. In that case, you can charge it independently with a power supply until it’s past the cutout voltage.
I think it’s all you need to know.
If you decide to buy a new battery or order one to be built to your specs, contact AlienRide or Evees, both in CA.