Contact Jerry Stiller on the availability of the 25X action which is the repeater - he may have them ready. North Shore Barrels ,a sponsor on CGN, can get you one. Sean posts on here as 'juanvaldez'.
There are lots of barrels out there - but if you want a good rimfire barrel have a look what's being used by RF shooters who specialize in accurate rifles. Checkout Benchrest Central/Rimfire section and RimfireCentral.
Lilja,Broughton,Shilen and Benchmark are the barrels to use. Expect to pay as much for a custom RF rifle as you would a custom CF - possibly more because there's more fiddling around with extractor cuts and other milling specific to RF builds.
An alternative to a custom would be a Cooper as you have said or an Anschutz 54 series repeater like a 1700,1710 or 1712. Or an older donor 54 action rifle for the action and get a barrel threaded on.
Any of these should outperform a CZ, but they should too !