Has anyone seen, built, or looked into building an axle driven E trike?

I'm talking about taking a a typical, common type of non-recumbent trike and adding a chain drive motor that drives the rear axle.

Most major brands of trikes come with a bracket for a coaster brake or a 3 speed igh (internally geared hub,) if the trike is not already equipped with one. When equipped with the cb or igh, the drive chain goes to the hub, and the hub has second sprocket and chain that drives the axle. When sold as a single speed without a cb or igh, the drive chain typically goes to a free wheel drive sprocket. The rear axle has room for more than one of these drive sprockets.

I'm thinking about adding an electric drive motor to a single speed trike, so that the motor drives the axle and rear wheel. I'd just add another free wheeling sprocket so it freewheels when coasting, but drives the axle when the motor is activated. First problem, after how to mount it - not insurmountable - is if I'm going to find that I need a much larger sprocket than will fit on the axle and clear the frame. I'm not finding much info on sprocket driven e-bikes from which to figure out what motor would be good and what kind of sprocket I'm going to need.

Most of the motors I'm seeing come with a small sprocket, like 11 teeth, but they run at pretty high rpms. I might need an axle sprocket so large it doesn't clear the frame.

So, has anybody here gotten into this yet?

I guess it's really irrelevant whether it's a single speed trike, or if it has a cb or igh, unless I wanted to utilize those brackets where the cb or igh mounts. Most trike axles could still take another sprocket.

The real problem is if I need a sprocket that is of too large diameter.

I noticed that there's a mid-drive unit on the market, designed for cargo bikes, that uses what looks like a smaller diameter geared hub motor. This has no spokes attached, instead being mounted in a bracket much like you've got on a trike. It looks like there's a sprocket (chain wheel is probably the better word) mounted on the disc brake mount, and this drives the bike. Seems that this would require an even larger sprocket on the axle, since the chain wheel is larger than on a small motor - however, since the hub is geared, perhaps it produces significantly fewer rpms than a motor? It's driving a wheel directly under normal design.

I'd appreciate hearing from anyone who's got a similar interest or who has already done the pioneering work on this.