"Titebond needs air to dry"
Air is not required if there are enough moisture absorbing materials close enough to the glue line. Using a 1/4" MDF cover sheet is all that's needed to use clamp time specs for press time, e.g. 30min for Titebond II.
An interesting aspect of MDF is that it is porous. I once made a 1/4" MDF box using internal vacuum to clamp it (no bag/press) and paper held to the outside would kind of stick to it, i.e. it works a bit like a mesh/screen cover sheet.
Another useful aspect of MDF is that its grain is very laminar parallel to the face. You can use too much glue (easy w/ quarter sawn) and, while seemingly stuck solid, the MDF will peel off the veneer. The image is my worse experience w/ bleed through (wasn't thinking quarter grain).
While the cold press requires a longer clamp/press time, I've done glue coverage tests w/ TBII and couldn't peel the veneer off if I left it in the press for more than a few minutes.
...Scott, you said the veneer peeled off, was it at the glue line or did it peel off with MDF on the back of the veneer. The later wouldn't surprise me if you glued the veneer to the softer/weaker MDF core (surfaced spoil board).