Hey there. Walter Here. My wife is disabled and I keep her in wheelchairs from the used market. We definitely don't have your budget, but you did get me to check pdf sheets on our latest cheap pair of batteries. In my experiences the Cheap batteries last her about as long as the expensive MK ones.... a little under a year or so. I just bought a pair of Raidon 1U batteries ($125US shipped). It could be that part of our problem is the 1U batteries themselves as they don't have the capacity of the larger ones and she runs them harder (deeper discharge) than the others would be. I'm thinking about installing anderson plugs but these batteries are only rated for 10.5A charge. You've got me thinking about different charging methods though. I do have three of the iMax B6chargers (RC combat warships). I'll have to look up the specs and see if they will do voltage limited charging, don't remember. Pretty sure they don't do float though. Watching a couple of the Hyperion chargers on ebay, but it looks like they go for $125 used. I wonder if there are some Chinese knock offs that have the Pb feature set.
I can't seem to understand the various battery and charging graphs. Haven't got the sight as of yet I assume. I work in IT and assume they are not hard to figure out. Perhaps I should watch some youtube videos. I did see that they have LifePo batteries for 1U but they are $850 and only increase the amps from 33 to 40. Kinda wonder about building some out of cells. Rebuilding some LIpo packs for my little drill right now. Need to get some better soldering irons. Currently we are doing the Pride Jazzy Select series and I have around nine parts/backups for her. Also have a Jazzy 600XL that I might consider playing with. I need to take the controller apart and clean the contact as it's a pain to turn on. It uses the larger batteries like you like. In my experience they run twice the cost though for new batteries. I generally buy stuff of ebay.
I do have a question that I have not found an answer to. I think it is possible to do a parallel tap on wheelchair batteries. The wheelchair itself uses a serial hookup to produce 24V, but I theorize that you could run wires and tap for 12V (at double the amp hours) for powering things like cell charger or gps. I'd rather like to hook up a 12V car cigarette lighter port for her. But I can't find anything on doing both setups at once. Perhaps I'm missing something. Perhaps I should just pull out some warship batteries and try a proof of concept. My big fighting warship is a H-39 German Battleship (laid down after Bismarck/Tipiz but never completed). My whole reason for the parallel tap is to keep the draw balanced across the batteries. I'm decen't with electronics, but far from a electric theory engineer.
Eventually I'd like to see her with better range. We have an unmodified Dodge Grand Caravan and I use a 3/4" 2'x4' plywood sheet as a loading ramp. The chairs don't do that by themselves but effort is minimal for me with the wheel assist. It's fast and easy. Got the idea from a guy who had a broken electric ramp and just pulled it down manually all the time. She doesn't drive, but loves to cruise around town and go on adventures in San Francisco and Berkeley. We live in a small town 70 miles from SF.
https://www.raiongroup.com/content/RG12350FP.pdf