I'd at least use sandwich construction between mast track and rear footstrap, but don't cut it off square. It should be tapered from in front of the mast track back to the front of the front footstrap, other wise you risk breaking the board at the junction.
When gybing and slogging, the front foot is often in front of it's strap, I've seen boards fail because this area wasn't stiff enough.
The thing is, to get any stiffness without a sandwich construction, the lay up is probably going to be just as heavy or perhaps heavier than with.
You'd need to do some real homework on this and make sure you're actually saving a bit of weight.
I wet out 4oz cloth on the table for the underneath layer, place on board then vacuum the corecell to that. Then I use 2 layers of 4oz on top of that at about 10 to 15 degrees off straight, with the two layers in opposing directions. This is also vacuumed on, the bottom gets just enough q-cell bog to sand to a flat finish, the deck gets a very runny q-cell mix squeegeed on to fill and pin holes. I don't worry about a true filler coat here as it's going to have a sugar deck anyway.
The impact area, top and bottom get a triangle of 6oz carbon, between tail and mast track at 45 degrees underneath the corecell. and patches of carbon under each footstrap.
This ends up strong and light, admittedly I don't weigh much, but some of my boards are 10years old and still going strong. My 90liter board is around 13lbs, but that's using 23kg/m3 foam, if you used 13/kg/m3 foam that weight would come down by about 2lb, and perhaps not quite last 10years.
I'm not sure what your 2lb foam is, obviously not a cubic meter, is it a cubic yard? These maths are a bit hard this time of night.
Hmmm now I'm puzzled, just did this.
Select to expand quote
michael@Mate:~$ units 2lb/yd3 kg/m3
?* 1.1865528
?/ 0.84277747
michael@Mate:~$ units 2lb/ft3 kg/m3
?* 32.036927
?/ 0.03121398
So if it's cubic yards it's way light, I don't believe foam this light is possible.
If it's cubic feet, it's on the (very) heavy side, and you may well get away without much sandwich construction. If you can get 1lb foam and use full sandwich, I think you'd have a better board.
Although it occurs to me, your foam may be the closed cell extruded not expanded open cell variety. If it's the closed cell stuff, I did make a board ages ago, with a sandwich bottom, reinforced footstrap area, and just 2 or three layers of glass over the rest of the deck.
It lasted OK, but the unreinforced deck dented fairly easily. It's so nice not having to worry about dealing with vents and their problems, that the extra weight is probably worth it.