Perhaps it goes to show how few folk pick up Model Boats mag these days? Per chance there is an article from Graham Ashby (very active on the Model boats forum) this very month who made a model from foam and decribes very well how he glued it together and covered it. I know allot of folk don't see the value in mags but I still do and they're worth every penny?
For me personally I tend to build in balsa / basswood because I can cut it with a knife and it sands very easy -I work in my flat on the coffe table in front of the TV! I've never taken Glynn Guests advice before now and used tissue paper as a covering for a full hull (I've only done it for small fittings like lifeboats) but I did this time and used it "paper mache" style using Deluxe water based "Eze Dope" which is a delight to work with and fills allot of gaps / low spots by addition of another "bit" of tissue to save filler. Personally, I bought a pack of ZAP Z-Poxy a few years ago which has done 3 or 4 hulls now, and for the same cost of a pack of coarse tissue -I got a pack of 80gsm fibreglass cloth the other day and went back to covering everything in that. I have not had the guts yet as a single man to buy a pair of tights in Tescos yet to try. Neither the Eze Dope or Z-Poxy have any discernable smell (the Z-Poxy is slightly sweet but no more offensive than some emulsion paints). Eze dope wash the brush out -Z Poxy throw it away. Both sand incredibly easy but I feel the Z Poxy will last longer and is the better choice for wetted parts.
I would say to carve a foam based hull then cover it you may have taken a slightly harder route to start with as a beginner, but not the hardest. But there is nothing wrong with your method and lots of folk round the world build this way (US guys seem to love it). You don't necessarily need a hot wire cutter (if you do -look-up model rail forums as they just love them for EPS and XPS). For me as an ex-model railway dabbler I found a very sharp kitchen knife (Sabbatier), or the blade pulled from a retractable break-off knife worked pertfectly while everyone else was fretting about mess with woodsaws etc, I had virtually no mess and clean cuts. Untill you sand of course and that will always create dust.
.....Bear in mind also I've only been modelling 30 years now so expect me to be stick in my own personal ways. I think there's plenty out there on 'tinterweb on this kind of stuff. You mentioned you might have a plentiful supply of foam so the best bit about modelling is to try for yourself -because if itworks for you it won't for someone else and vice versa!!!! Don't be afraid to try things yourself because that's how you learn.
Cheers,
Rich