I'm assuming that's a sealed-lead-acid (SLA) battery. If you have (or are willing to learn) the skills to work with some lithium-ion cells, I believe you could replace it with a smaller pack, probably 3S (three in series) with a small charging/protection circuit added. I doubt that you need the 7.5Ah capacity, but you'd need to make sure your pack can supply the brief high current you need to run the starter.
You could probably skip the engineering part and try using a lithium jump-starter pack instead. It would have a charging port that may be compatible with your charging supply, and a short jumper cable lead. You'd have to separate the "charging" from the "starting" side.
Note, I have not done this myself, and I'm not familiar with your setup, so take what I say with a grain of salt. I'm a noob to the MB world. I do have some experience with li-ion though. What I'm suggesting would take some work on your part, and you do have to really understand what you're doing with li-ion pack charging and discharging, both for fire safety, and to make the cells last. So this is really just a suggestion of something you might investigate.
Note that if you use one of the little jumper packs, you'll also get USB charging ports as a bonus. Some of the packs I have also have DC output ports at multiple voltages, so you could charge a 19V laptop, or run 6V LED lights from it, which may be a useful feature.
If I were engineering an electric start system for one of these bikes, I'd almost certainly go with lithium over lead-acid just for the weight and bulk savings.
BTW, that's a really sweet looking bike. I love it!