Never been "touristy" caving in Crete but i'm aware that there's plenty to go at. The 3000 or so caves seem to be split into two types;
a) higher altitude stuff, very vertical
b) lower altitude stuff, mostly horizontal
AFAIA there's only one major cave that does both called Tafkoura (650m of vertical to a 5km long streamway!) in the central mountain range (second longest cave in Greece). The deepest in Crete is Gourgothakas at 1208m deep (deepest in all of Greece) which is in the White Mountains to the west of the island.
I haven't had much dealings with the HSS but i have with S.EL.A.S (athens based) and they are very cool and helpful.
I'm sure you'll have a good trip.