I'm working as a European citizen in Florida as an instructor myself, however I do so with CFI/CFII/MEI (FAA) and a work permit per my Visa.
All the things mentioned in this topic, I find the most gray area (rather black area) is the working (even though you aren't getting paid) as a JAA instructor flying with students.
I'm pretty sure that you getting hours for flying as PIC with a students counts as a commercial operation, and if you're not doing it as flight instruction, you would need to do it under a commercial operators permit and hold a FAA CPL.
I agree that the 20hr requirement does not count, as you are not submiting anyone for a FAA part 61 practical test.
Also, as long as a FAA CFI is signing off the endorsements of the student for Pre-solo flight training etc, then there is no hour requirements there either.
The big no-no that I see, is what I'm pretty sure is considered work, in black and white by the FAA, from what you have told