Almost you will save 1/3 of the cost. Try for these hotels - Tamarind Anjuna, Verda Caramona, Sterling Goa Varca. These are descent hotels with cheaper rates.
I visited Goa in December and was still able to find a good hotel deal for 4k for 5 nights for a couple.l for a 3 star accommodation with all amenities like pool, snooker, breakfast, etc.
May and June hotel cost would be little lesser than the peak season in Dec but that's the time to party there, suggestion would be to visit before Dec 20 where you still get good deals and also the peak season activities.