I just came across this thread.
Check out Kalymnos.
http://www.kalymnosdiving.gr
https://www.scubakalymnos.com
Kalymnos is pretty easy to get to from Rhodes, not really on the standard tourist itinerary, and well known to rock climbers and wind surfers.
Also, traditionally a prime occupation on Kalymnos was diving for sponge.
Might be a fit for you.
(Disclaimer - I don't dive, but the outdoor activity focus on Kalymnos and it's history brought it to mind).