You could adapt an electric tool battery for the job. One of those 4Ah jobs from Aldi when they are on special. They have their own built in cell balancing and are never likely to reach the 20vdc fully charged, so a high cell voltage run away is never likely to happen. I've never measured the low cell voltage cut off but as long as it is 2.5v or less you would be fine, 2.5v x 5 cells in series = 12.5v, but that could be altered if needed. The maximum amp draw might be the catch, but that can be altered as well if needed.
That way, a flat battery just requires the battery being slotted into the charger for 1/2hr to get enough back in to start the bike. You wouldn't want to fully charge it, I can't see the electrical system appreciating a 20v hit
You could always build your own lithium battery out of Headway cells or even model plane cells ..... They don't make 12v electric bike batteries and the drop in lithium replacement bike batteries are a tad questionable when it comes to build quality. Maybe one built to race bike standards, but the price might take your breath away