You've obviously thought this out already, but have you considered using hobby LiPo packs?
It sounds like your pack will have 15Ah. Why not take three of these plus a three-fer, 10 minutes of soldering and call it a day?
Not really. I am building a 15AH pack, but I'm sticking with Samsung ICR 18650s. Several reasons for this:
1. I'm rebuilding an existing pack with a proprietary BMS I can't get any information about (even the tech guy I talked to at iZip didn't have much information on them). The BMS and the rest of the bike interface as well. So the best option is to rebuild the pack with the same chemistry batteries, so I can reuse as much of the system as possible. I'm not out to re-engineer the entire bike, just get it working again. Upping the capacity of the cells (keeping the same ICR chemistry) won't affect the BMS any, just the charge time and range.
2. There's a good chance I will turn around and sell this bike. Hobby LiPo packs are not suited to anything I might let anyone else use, IMO.
3. Learning to spot weld cylindrical cells is useful for building other types of packs, specifically my preferred LiFePO4 chemistry.
4. I like my dwelling place not-on-fire.
It mostly comes down to the fact that I'm not currently convinced that hobby lipo packs are particularly safe or reliable for use in ebikes. I know they're used a lot, and most of the builds I see with them scare the sh*t out of me. No BMS, high voltage bulk charging, massive numbers of packs crammed together so tightly that if one overheats the rest will follow, etc. Almost always followed by a comment about how this is a really bad idea and you should never do this. I'm also iffy about the cycle life on them - hobby packs tend to live short, hard lives, so I'm not sure there's much data about their longevity.
I'm sure you *can* build a perfectly good ebike power source out of them. They're energy dense, and I'm sure you can get a perfectly good BMS and balance charging system going for them, but that seems to be the exception rather than the rule. But, for rebuilding an existing 18650 pack, they're not a good choice.
I try to do things right, not cheaply. On the "Powerful, cheap, good" scale, hobby packs seem to be shoved as hard into the "powerful, cheap" corner as you can get. If they were so awesome, I'd expect ebike OEMs to be using them, and they don't (at least, not that I can find). Though some may be using pouch lipo cells.
I'm open to discussion on this point, but hobby packs seem to be crammed firmly into the Endless Sphere mentality of "I want to go unsafely fast on a cheap bike as little money as possible, YOLO!"