Hallo again Finley.
Do you have a big flat white wall you can draw on - or stick a large piece of paper to?
Here's some parameters: 'Reach' is measured from the front surface of the seat back to the furthest forward position of the handle.
The bigger the front wheel the better traction and lower rolling resistance you'll have - but you have to trade wheel size against the eternal problem with hand crank propelled wheelchairs - lack of traction. What you're building is a front wheel drive tricycle which has almost all of the rider's weight over the rear wheels. So you want the front wheel to be as close to rider as possible without clashing with the feet. Most clip-ons therefore use a twenty inch (406) wheel - for which an enormous range of tyres is available. Including off road tyres.
Clip-on hand-cycle units cannot fit on a regular scissor action folding wheelchair. They will only fit on a rigid chair. And rigid chairs are invariably expensive - if not custom built. This rather goes against your stated aim of making it inexpensive...
Plotting your machine in profile onto a wall is the best way of getting a quick understanding on the shape of it. Looking at your sketches you'll need to move the front wheel forward and the 'bottom bracket' rearwards. The relationship of the steering axis and the tyre's contact point on the road is CRUCIAL to the safe operation of your trike. Research: 'head angle', 'trail', 'castor effect', 'fork offset'.
Brakes. Coaster brakes are almost universal on hand cycles. You'll definitely need a second brake, either rim or disc. It'll need gears, and the only way to get gears with a coaster brake is with an internal geared hub such as are made by Shi**no and Sturmey Archer. You will definitely need to consider where you mount the gear and brake controls. Mount them on the handles and they'll start deteriorating with the first turn of the handles. Mount them on the frame somewhere and your rider will need to take her hands of the handles to use them. Hand cycles devour cables.
Purpose built upright hand trikes have a longer wheelbase to compensate for the lack of weight over the front wheel. But if you move the wheels rearward on a wheelchair you might make it a better hand tricycle but destroy it's ability to function as a chair. Some chairs have a plate on each side with two sets of wheel locating holes in. Locate the wheel forwards to use it as a chair & pop them in the back holes for use as a trike. Easy to do with standard QR wheels - but adds cost...
Very few people use handles which are flat/horizontal. Most use handles which are close to vertical - about 10 degrees or so camber.
If you need to know any more than this I'm going to have to charge you.