Bill,
This shouldn't be too much of an obstacle.
You should be able to get a maintenance task approval to do it after having some training signed off by your maintenance provider, especially a Part 145 shop, then you should be able to fit and remove the stick, then as far as the duplicate goes, it can be carried out by another rated pilot including a PP. Refer CAA 43.113 (b)(2)(iii)
Then it will have to be documented as per 43.113 (c)
Make up a worksheet that contains all the info required by the rule and set it up just for the duals
I would contact John Keyzer at CAA and talk to him, I would be surprised if he wasn't helpful and he should be able to guide you in the right direction.
As far as taking the stick out when you send someone solo, that would a bit of a grey area, possibly adopting a process where everything (seatbelts and cushions) are properly secured could be a way around it.
I know of pilots who have approvals to fit and remove Hughes 500 Duals including the tail rotor pedal assembly, so I can't see how a Cub rear stick is going to be an issue.
Cheers
Jim