Your Stark battery is a self contained unit so it's hard to tell what BMS functions are built in. I would guess, if sold as a drop in unit, it should handle most situations. I looked at the website to see if I could get more information but a technical manual is not there. Might pay some dividends to call and ask if "Maximum Charge Voltage Disconnect" and "Low Voltage Load Disconnect" are built in functions. If so, what are the range of voltages.
As for a programmable charge controller, they do exist as DC-DC charge devices. These are designed to limit the current flow to "X" at a set voltage but the problem is that most of those are designed for lead acid batteries going through bulk, absorption, float, equalization, which a Lithium doesn't need. Some allow a limited amount of program options that allow voltage set points that might work. Here's one made by Xantrex.
The high voltage disconnect is 16 volts - load disconnect is supposedly at 10 volts, however the battery case says 9.2. Either way I don't plan on running below 11. I have an alarm set up in the Xantrex to go off at 30% and in theory could set up a load disconnect.