A lot of places now are also wary of accepting largish groups of same sex bookings - ie a group of lads, or girls together as they have been known to disrupt other people in the hotel when returning after a drinking session.
Looking at that list of age limits, it doesn't leave too many choices given the age of the group.
Germany, Italy, Portugal and Cyprus are probably the best bet as the first 3 start at 16 with Cyprus being 17yrs to drink legally.
There's a couple of Scandinavian countries there too but could be expensive.
Ayia Napa club prices are very expensive but the bars around the Square are open till past 2am.
However, going off past holidays we've taken I would say Portugal may be a good place as I recall prices of food and drink was always a little lower than mainland Spain and the islands. Italy was expensive but I haven't been to Germany for many years.
If there is any hint of trouble in Ayia Napa, the hotels and police are very quick off the mark as it got a bad reputation a few years ago and they clamp down heavily.
You may know them all personally but having worked in travel for many years in UK before moving to Cyprus, I've had to listen to parents sobbing their hearts out on the phone when they find out their kids have either been arrested or threatened with being thrown out of accommodation if they didn't pay for the damage they had caused. I personally know of 2 incidents where guests were locked up in Nicosia prison for 28 days (1 for damages and the other for falsely making out they had lost a camera whilst on an excursion). The camera was found in their accommodation when the 2 guests were separated for questioning. The High Commission got involved but they still had to serve their sentence!
Given the fact your son's account on here was already closed because he was under age only confirms that more attention needs to be paid to the small print :-)
Good luck but I reckon your hair will be grey by the time they return