Is there anything special about Slovakia why you'd need to do your FI rating there?
I don't know answer to your query, but if I were you (and may do in future as well) I'd just get in touch with one of handful Czech FTOs and do your FI rating there.
AK Zbraslavice sound reasonable to me. They use mainly Z-226 and Z-326 - famous 'Trener' aircraft for FI rating, but have others. Tailwheel, if you didn't know.
When I swapped few emails with one guy at SK CAA, I got to know this funky thing with FCL. They do however recognise JAA papers for comm jobs in Slovakia. That doesn't imply it should go both ways. If it did, they'd be fully 'in', not just JAR FCL compliant.
If you want to instruct in Slovakia and you do what you say, it should be fine, wouldn't it? I'd go the Czech route. Good deals to be had compared to FI rating in the UK. Just bear in mind current job market.