This battery-powered clip-on doo-hicky may not extend your mobility horizons, but it should make your existing ones easier to handle.
I have been struggling up the uneven slope to my office lately, and searching for a little oomph to avoid my shoulders becoming any more knackered thatn they already are. The choice was between a hand-bike attachment at the front of my wheelchair and a SmartDrive underneath.

The former option — several makes are on the market — effectively upgrades the chair into an electric trike. Another term for it could be mobility scooter. I make the comparison only because your hands move from the push-rims to handlebars and all the power then comes from the front wheel. You just steer it. I once tried out my Dad’s mobility scooter and froze half to death after half an hour excercising only my right thumb. That said, the combo does look and perform much better than a scooter. It also lifts the front castors of the ground so you can try it out OFF ROAD!
With a SmartDrive, your hands must stay in contact with the wheels, if only because the thing will push when you start it and only stop when you tell it to. If you come up against a stone or tree-root and fail to avoid it, stop or lift the front castors manually, it will keep on pushing until, in a worst-case secanario, it tips you onto the ground and runs you over. Your own chair. Oh the indignity. But at least the blood keeps flowing around (and potentially out of) the body.

You control a SmartDrive through a Fitbit-style wristband with a Bluetooth connection. This feaures an accelerometer that reacts to taps on the push rim. Two taps to go, one to stop accelerating and two more to stop. After a couple of near disasters pushing/driving up my uneven slope, I have the hang of it. It helps if you (counterintuitively) lean backwards. I will now trial it at the local beauty spot where I exercise the dog; if that works, which it should, everything else will be a bonus.
I will also use it in conjunction with my FreeWheel, which will get round the castor problem. That should make for quite a nifty combo. More later.