If you reap any cost savings, you'll end up paying for it 10X over in time and frustration, or suffer longevity in lifespan or travel distance.
Merely adding up # of cells needed in a battery, is nothing compared to assembling a pack, using a spot welder, into an appropriate size fire-containing metal enclosure, custom charger, battery health monitor, motor controller, etc. You'll be DIY what others have spend cumulative lifetimes worth of engineering and experimentation to achieve. HOWEVER you can leverage that, if you frequent an eBike forum so you can copy some existing designs and ask questions of those who build these as an obsession, but they will probably tell you the same thing, to buy ready made components until you know of reasons to deviate and improve on those.
I'd never think in terms of "just need more of them" when choosing cells. The inexpensive ones aren't just low current capacity, they're typically fraudulently overrated so at the end of the day, you aren't really getting much if any more capacity per dollar, more so that it's just building a bigger, heavier battery.
However, it's really easy to find batteries capable of more than 2A current. One option "might' be harvesting them from new cordless tool battery packs. You can sometimes find these battery packs deeply discounted, for example when a tool manufacturer switches over to a different battery format and closes them out, but I'd make sure to choose a major brand or one known to at least have major brand cells in it, often determined from a youtube battery teardown video, not using those 3rd party generic battery packs which are practically always shown to have poor capacity relative to their specs.
It is a bit beside the point, that this is not the right project to learn about Li-Ion battery packs, particularly on a vehicle where you are traveling and located so close to the battery. It could become quite the fire hazard if 100 cells were to cascade fail, then you are stranded, fire department comes and puts out your bike fire then a wrecker hauls it away and bills you for that service.
If you want a reasonable price point for travel or just more fun than burden, I'd sooner recommend a gas engine scooter or motorcycle.