I looked at the SRAM i-Motion 3 hub instruction sheet:
http://cdn.sram.com/cdn/farfuture/_E...Ins_E_6_06.pdf.
It doesn't give the actual gear ratios, but it says it has 3 gears with jumps of 36% between them, giving a total range of 186%. It is available in 3 different hole counts, 28H, 32H, and 36H. The 28 would be perfect since the existing rim is a 20H. One additional spoke could be added between each of the existing spokes except at the valve stem, giving exactly 28H with the existing rim, re-spoked. The OLD is 130 mm. It has 2 twist-shifter options. It has 3 brake options: coaster (back-pedal), none, or disk. The good thing about it is that the shifting cable exits the hub parallel to the chainstay tube of the bike and within the frame width, not outside of the forks the way the S-A hub does, so this may provide the clearance we need for the folding. Further investigation needed.
The SRAM G8 has 8 gears and option for a coaster brake, but the specs at SRAM don't give the necessary facts, such as the OLD. I think the shifter cable also comes out of a hole in the side of the hub parallel to the chain, not out of the end of the axle.
G8 | SRAM
This listing at Amazon says it has OLD 135 mm:
http://www.amazon.com/Coaster-Brake-...ywords=SRAM+G8. The SRAM page says it has option for Gates belt drive, so maybe the Gates sprocket can be used with the Free Ride's belt, or the Free Ride jackshaft sprocket could be changed to a Gates, maybe. Lots of maybe's here.
This listing on Amazon says the G8 has OLD 135 mm.
http://www.amazon.com/Coaster-Brake-...ywords=SRAM+G8
Sheldon Brown has a page about SRAM/Sachs IGHs:
Sachs and SRAM Internal-Gear Hubs
Aaron's Bicycle Repair in Seattle, Washington, has a lot of good info on IGHs. They sell and service them. Note the advice about lubricating them very well in areas that have a lot of wet weather.
http://rideyourbike.com/internalgears.shtml. Good pictures there.