Sorry if we are coming off a bit harsh here, but sometimes the truth is harsh. I really think you paid for a battery with some bad cells, live and learn. They sag under load, and the bms shuts off.
You don't have to go spend money on a charger, but I do recommend having one of the inexpensive 50w ones around if you are into EV's or other battery stuff. They can be damn handy.
You can help that battery balance faster, by simply rigging a car turn signal light bulb to two wires, and discharging the highest voltage cell down to the same level as the others. Then put it back on the charger, letting all cells get more charge. The one high cell turns off the bms charging for awhile. Or, just put it on the charger for a week or so. Less of course, if it's not so bad out of balance.
Nothing to lose by balancing it up, and seeing if that helps.
The other educational thing you can do, is go to You tube, and watch a vid on how to test cells for internal resistance. You'd need some tools for that, but nothing real expensive. The light bulb, or a small motor can be your discharger. Testing resistance may pinpoint a single cell that is much worse than the others.
My guess is that you will find that all the cells are toast, with no capacity and high resistance.

300 cycles is an old battery for that chemistry. Even lifepo4 can be killed with 250 cycles, I did it.