I don't see how the IO portion of your gadget is going to run faster than the system clock. Sure, you can run the logic at a submultiple of the system clock but, in the end, everything needs to be synchronized to the system clock. There are usually clock managers on-chip for the very purpose of creating phase accurate (sub)multiple clocks.
But I still don't see how the internal logic, running much slower than the JTAG IO, is going to work.