Others will disagree, but here's my current thinking on wood veneers.
The 2-ply you're talking about is sometimes apparently referred to as structural veneers, and it's my understanding a couple of the boutique builders use it in their boards. From reading what the vendors say about it, it appears the underside layer is usually a different wood and is usually laid like plywood, at an opposing bias.
I say "usually" because I am no expert on the subject and I'm only familiar with the examples I found.
If so it would be both stronger and stiffer; the latter making it tougher to work with when trying to bend it into compound curves such as on the deck side of a shortboard nose where in addition to the rocker there's also some roll to the rails.
For laying the veneer, Greg Loerh's original gameplan was to lay the veneer directly against the foam on the bottom of the boards and to reinforce with fiberglass on the deck side, leaving the edges bare so they'd fair into the rail profile better.
I tried that once and - due to a couple different errors I made with my glassing, ended up with water damage to the veneers from a leak. Although that board still surfs fine 5 years later, it's a mistake I never made again.
The two things the fiberglass does is add to the adhesion, and add to the support or stiffness. The bad rap that doing veneers on both sides got was that they're stiff, which is why some builders only use it on one side.
So based on my experience with them, on my last veneer I used a light non-woven veil for the waterproofing and adhesion because the structure of veil is better than wovens for both functions. I only add fiberglass cloth on the core side in the areas that I specifically want to reinforce, like the contact area of the deckpatch or fin patch. Not only does the combo turn out lighter, but IMO it's also easier to tweak the flex aspect so long as the core itself isn't too thick for that - which is usually the case with most of my designs.
The other thing about doing veneers that I'd tell you is that you only need enough resin to wet out your backing. The vacuum will do the rest. On my first veneer I made the mistake of being nervous about whether the edges would hold so I added more resin at the edges and I didn't tape off my rails. It was a PU
blank so the vacuum pulled the excess all over my rails, albeit unevenly. It was a PITA to recover from that error so I never made it again.
Now I use the "revised" method for veneers of using a little spray adhesive to stick my backing to the core side of the veneer and without trimming the edges. Then I wet it out with some resin by using a foam roller on it, using just enough resin to barely wet out the backing. If the backing moves around a little during this process it's okay because I don't trim it until it's wet out. Flip the veneer onto the blank and tape it down with some masking tape and you're good to go.
Run your vacuum port and breather on the dry side of the board, not the wet side; and smooth your bag so there are no wrinkles (and thus, nowhere for excess resin to seep). That's something a lot of guys don't do, and then they wonder why they get the uneven surface from that excess resin.
IMO doing a clean veneer is way easier than doing a clean lamination.
