@deacon
I've tried friction drive , but it was a gas motor on it (veeeery old thing - made some time after WW II). It had great acceleration as well. Three or four years ago , I've set on a e bike (brush less hub - made by Crystalyte) and from that moment , I'm into electric vehicles. I've had only one e bike so far and I had to sell it (finance problems) , but I will get (make) another one (soon I hope). I have , also , tested (whenever I got a chance) , many different setups on e bikes and researched a lot (and lots of people lost their will to live in a process - I was very persistent with questions and boring).
I know that building bikes keeps you busy , so you try different things (since you can't drive any more). Torque overcome hills and that is directly connected with a geometry of motor , not Amp or Volt rating. In lack of that , excess power is needed (and wasted). Lost power also hurt the range. That's where talk of efficiency comes in place. Chains can be unreliable , but less than friction drive. Brush less hubs beats them both. Of course , proper installation and some know-how is needed. Now , in your case (balance problems , not much speed needed , problems with longer pedaling...), there is a few ways to solve it. First you can use any drive you like (just reliable enough) and build a trike (and by that , I mean soft tails on rear - kind of APAX - plenty of room for batteries between rear wheels). It is stable , allows leaning and can be wide as you are, (22" or so is enough) , so it won't be a problem trough narrow passes. Also , you can loose coaster wheels. Second, if you use plain frame , you need to build VERY reliable system (and you going for chain drive now) , which means that everything custom should be well designed (for the purpose) and put together in precision manner(properly aligned chain sprockets and healthy chain don't brake , unless hit , excess power or internal failure , invisible at check up). Not saying that you can't do that , it just seems to me that you avoid welding and machining , which is necessary for these kind of stuff. Third , you can use plenty big(AH) batteries and feed the Amps to inefficient system (Volts are limited due to required reduced speed). This involves a lot of weight (if SLA) , so that is the worst solution.
Some friends and I built , few years ago , e bike from an old frame (similar to yours) and car starter and car batteries. Talking about efficiency , it was one of the most inefficient I've ever heard of , but it could pull a house and throw you on the back at start (it had some relays instead of controller so it was on or off and delta-star wiring for speeds). Range was (at relatively flat) only about 10 km (~7 miles) and speed was , well , very unsafe (we passed by some speeding scooters as if they were parked). It was heavy as planet. Point is that even inefficient system can work , you just need to figure it out, how to use best of what you have. Oh , bike broke in half after some jumping from improvised ramps , in case you wonder what happened to it.
I'm only replaying on your posts so often, because I follow what you're doing (it is very interesting to me and sometimes , you remind me of Don Quixote ); It is like favorite TV series , so the first thing (after checking mail) is to see what you're up to.
To resume: proper gearing and good construction and design of the system (whatever system it is) and you'll be ready to go places.
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