This is a subject I've been thinking about for some time now for my live aboard sub ideas as well as for smaller craft. Most insulation choices out there are porous to external air. This means that it can get wet and oh so moldy. Also if you ever flood your sub in any way you'll have allot of work to do. Urethane foam may work well for some designs. I've seen some become old and powdery after a few years but that maybe because of a bad mix and/or UV damage. Urethane foam wouldn't work for me because I want my subs to be able to be used as hyperbaric chambers for both general health benefits at 2 atmospheres as well as for divers with the bends. With this in mind I wouldn't expect urethane foam not to stand up to the internal pressure of the sub(s). If you have a dive boat that is also a submarine that can take care of a divers hyperbaric chamber needs at the dive sight I know it could save lives.
One insulation type with a reasonable R value that is sealed and can compress under hyperbaric pressure, is a foil covered expensive version of bubble wrap called bubble foil insulation. One brand is call Radiant Guard.
You can find bubble foil insulation at most large hardware stores. One problem though is that because it will compress under pressure it won't help your buoyancy if your sub starts to flood.
This is why I was thinking syntactic foam may be the answer for all my requirements. From what I understand syntactic foam would not compress under pressure. So if your sub floods it will help in your buoyance as well as keeping it's shape and insulation value if internal pressure is raised. In addition to all that if water and air can't get into the syntactic foam then you won't have the mold problems I mentioned or the need to replace insulation if your sub floods. Now since I have not as yet worked with syntactic foam I would love to hear any bodies thoughts on this that have used it as well as others.
The great merit of society is to make one appreciate solitude.
-- Charles Chincholles
Being alone in your submarine can be a wondrous thing.
Brent Hartwig