Yes, we live in Anchorage. From everything I've read Utila seems more touristy and crowded than what we are looking for.
Utila is hardly touristy or crowded, but if you want real off the beaten path- sure- go to Cayos.
I am reminded of my visit to your namesake, Alyeska Resort. We came into your town, Anchorage, to see the ceremonial start of the Ididadog Sled Race. The streets were absolutely jam packed. Some crusty looking locals picked their way along muttering under their breath- on the sheer edge of going Postal over the pressing crowds. Even Steven Speilberg was there. An hour later, the streets were absolutely deserted. So, I might understand what you want in terms of not "toursty or crowded".
With all of those new divers, I wonder if the condition of the surrounding dive sites have been compromised.
Remeber- it isn't the volume of divers, clumsy or not- it's the sedimentary run-off from development. The best condition for these local shallow reefs to grow was on the South side of Roatan, stretching from Dixon Cove to Calvin's Crack. (The airport to Oak ridge). Unfortunately, this is beginning to feel the effects of development. Such reef structure on Utila are smaller in concentration and size.
I like the "remoteness" of Guanaja but haven't read many positive things about the diving.
Divers have not returned in the same numbers only and precisely because the two larger resorts were fairly well devastated after Hurican Mitch in 1998. I can assure you that the diving is quite good, although limited in service by only a few very small operations. Check out Dunbar Rock. Remote enough for ya? VILLA at DUNBAR ROCK: Guanaja, Bay Islands, Honduras. The connections to get there from Roatan make the travel time expand comparatively. (same issue with Cayos)
Are there places in Utila where you can get away from the crowds?
The population center of Utila is concentrated in a small area. The rest of the island is undeveloped. It still aint Grand Central Station.
I would highly recommend a trip there now as it will change very soon.
There is a resort on Roatan down in Oak Ridge Barrys Homepage , that although too primitive for most tastes here, might be right up your alley.
If you want remote and unspoiled, also consider Los Roques and Speyside, Tobago. There are many other great dive locations in the Caribbean, but they are poorly served by dive ops- if at all.