Never used a EFK barrel, nor heard from anyone who has...
That being said, you are correct on the barrel size. The SP01 family uses a 40 barrel reamed out to 9mm.
Briley was making barrels there for a while, but I'm wanting to say they were the smaller variety as well. You can make those work, though it'd require changing your bushing out for a smaller one. The Briley setup is also a gunsmith fit affair.
I can't remember if a TS barrel will fit a SP01 or not. Thinking not, but if I were you the first call I'd make would be to Angus at the CZ custom shop - www.CZCustom.com