Yes you are correct! I can't tell you how many people don't get that.
It's not that you are penalized for being "single" it's just that hotels rates are per ROOM per night, not per PERSON...unless you are talking about an AI where they do charge per person. So that means you have no one to share the expense of the hotel room.
Also Compudude, two-tank dives are the standard on the island. However, most ops have afternoon dives available now that it's high season and we will begin daylight savings time this weekend..but OF COURSE they are going to cost you more money which will most likely put you over budget.
If you are expecting more than 2 boat dives a day for a week, plus hotel, plus food, plus airfare as a single for $1K or less, it's going to be challenging unless you go with a high volume operator such as Dive Paradise who offers a third tank for very cheap. Keep in mind that that "cheap" third tank is not divers choice and it's a 95% chance that that it will be on a big boat with alot of people. AS Several have mentioned, it just depends on what's important to you.
I wouldn't give too much weight to the unlimited shore diving. Shore diving here is great for check-out dives, but after that....well...you'll see.
If you can find a buddy to go with you, you'll be able to save literally 50% of the hotel cost and have more for diving and food