It's tough to arrange your own diving in Cuba, but it can be done. Most of the dive shops are government owned, and in my experience, they just don't answer emails any more, no matter how far in advance you try. Maybe phone calls will work better. They are really just old school. They prefer people to just come into the shop and arrange their diving. Doesn't hurt to try though.
I first went diving in Varadero in 2002 and even as a brand new diver, it was only so-so. We did Havana as a nearly 24 hour trip and it was amazing.
I went back in 2015 and went diving at the Bay of Pigs, which was ok, and Jardines de la Reina (Gardens of the Queen), which was fantastic (link to my review and photos below), as well as spending a few days around Havana.
I went with my LDS to Marea del Portillo last year, and it was ok. Not a lot of big life. The scenery from our hotel of the sea and Sierra Maestro mountains where Castro laid in wait before his Revolution was beautiful. The area is very quiet, including the nearby town of Pilon.
From what I've seen as well as heard, the only pristine diving is in Jardines. The rest of Cuba is similar to most of the rest of the Caribbean.
Have you considered doing a liveaboard plus spending time before or after around Havana? We did a 10 day trip including 6 days on the liveaboard, an overnight trip to Bay of Pigs, and 3 days in Havana.
I had managed to arrange my diving by email (and in English) with a dive shop in Varadero the first time around. I also arranged the Avalon liveaboard for myself and friends by email and they're very responsive and communicate well in English. I had tried every dive shop around Havana by email to no avail for a while, and Avalon put me in touch with the great dive guide/casa (home) that we stayed with and there's contact info in the link below. The husband, Osnedi, does the dive guiding, provides tanks and fills, etc., and speaks English decently, and his wife Yaquelin makes the amazing food and answers the emails promptly - only in Spanish. I used Google Translate to translate my and her emails back and forth, and it was easier than I thought.
A 5 star hotel in Cuba is about equivalent to a North American 3 or 3.5 star, so you would be well advised to go for only 4 or 5 star resorts/hotels. The comfort, amenities, and especially their access to good food and spices is affected greatly. The best food is at a Paladar, a family run home restaurant, which we went to sometimes rather than having dinner at our resort, and they cost only around CDN $6 - 8 total for the two of us even last year.
I think there are still humanitarian trips for Americans run out of Ontario or Quebec where you are pre-paid at a resort and spend a little time at a hospice or other facility. They could probably arrange diving as well?
Sorry if I'm too long-winded. Cuba is absolutely stunning. Have fun planning!
Jardines de la Reina, Cuba Trip Report - September 2015
Cuba 2017 | Facebook