I like the idea of reveneering over the old veneer. While there are pure veneers to work with (ick), I tend to favor the pre-glued veneers--either PSA (pressure sensitive) or iron-ons. I realize it doesn't sound as secure as using hide glue and a vacuum press (and it probably isn't) but you aren't making something that is going to suffer a lot of abuse (and how many of us have vacuum presses anyway?). B'sides, its a helluva lot more secure than I guessed before actually using it.
I tend to think the heat sensitive veneers will probably work better for you--you can get it trimmed and squared up, and then apply heat. I've used PSA veneer to edge band a desk--2" veneer cut back to 1.5". Trimming is relatively easy with a very sharp knife and some touch up with 400 grade sandpaper. I also highly recommend the rub on poly coatings. Very easy to apply and you get a great finish with 4 or so coats.
I tend to think the heat sensitive veneers will probably work better for you--you can get it trimmed and squared up, and then apply heat. I've used PSA veneer to edge band a desk--2" veneer cut back to 1.5". Trimming is relatively easy with a very sharp knife and some touch up with 400 grade sandpaper. I also highly recommend the rub on poly coatings. Very easy to apply and you get a great finish with 4 or so coats.