I seriously doubt your timebuilding needs to be at an ATO as it does not constitute 'formal' training.
As far as I know you can go to any ICAO member state for timebuilding.
I would suggest you keep good records though including daily receipts or print out from the billing system so you have additional evidence corroborating the hours in your logbook.
But to answer your question:
There are two other schools on the field in Naples that rent aircraft.
And one on Marco Island if I'm not mistaken.
Then again you may look to rent elsewhere and fly to Naples and get a tie down spot from the airport authority.
Gives you a whole lot more flexibility.
Find the most economical airplane in the state and still fly it out of Naples.
http://www.delandaviation.com/rentals/
* I have no affiliation with the above mentioned school.
Just provided the link as an example of (relatively) cheap rental
I just checked online and tie downs are $200/month for '!non-tenants'.
Last edited by B2N2; 24th May 2017 at 00:51.