I've never tried it but I wonder, couldn't you just buy a 3S, 4S or 5S lipo, unwrap it and reconfigure the cells to parallel?
It is certainly possible. I have actually already done it a few times back in the DNA30\40 days when building the BAP\Tibs-II.
Problem with that is separating then re-soldering the cells. I'm a little "squirrely" about soldering them, let alone taking it apart in the first place. Mr. Murphy is my constant companion. It would be so nice to find a pre-made 3000 or 4000 mah pack, but home brew looks like the only way to get 'er done in this case.
Yeah, that is the thing, soldering those things does make my backside pucker up a little, unsoldering just doubles the pucker. Also, with pre-made packs they often use a VERY good double-back adhesive tape to keeps the cells together. You most likely will have to pry those cells apart to get all the polarity tabs oriented the way you want them. Tech grade Isopropyl helps release the adhesive, but it still can be quite the bear.
Dont give up on finding a high mAh 1S lipo though, they do exist. Do consider "Hardshell" packs made for RC cars/planes etc, you just have to take the shell off - but the same adhesive issue often comes into play.
Another serious consideration is "Saddle Packs". They can sometime be misleading in the way the vendors label them, but if you study it hard you can figure it out. For example they might call "the pair" a 7.4v 2S3P, when in fact it is two separate 3.7v 1S3P packs. The nice thing about saddle packs is they are often much shorter, but also a little thicker.
For example this battery is labeled as 7.4v 2S3P, but in fact it is two separate 5000mAh 3.7v 1S3P packs (it will make 2 mods). The wiring harness they include is what puts the two packs in series to make "7.4v 2S". Look at the dimensions, 70x47x25, and remember that once you take the hard shell off it is 1-2mm more narrow and 1-2mm thinner, and 3-4mm or more shorter. Look around, this is just one example, there are more.
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