hesster, if you haven't yet applied the veneer, I'd like to make a suggestion....
Because of the decision to use screws to assemble your enclosures, you will most likely have problems with them telegraphing through the veneer. There are a couple of reasons for this. MDF will expand and contract in thickness due to humidity, no matter what you do. Whatever filler you use to cover over the holes will not contract at the same rate, so you'll have a "dimple" or slight "crater" where the screw is.
I built a set of test enclosures years ago to evaluate fillers. We filled screw holes with 3 different wood fillers, dry wall compound, plaster of paris, dental plaster, bondo, PVA/sawdust paste. They all telegraphed the holes over time. It is permanent.
I would suggest (if you can) to pre veneer over your enclosures with as thick a veneer as possible before applying a thin paperback veneer, in order to mitigate the telegraphing that will inevitably occur.
I'd hate to see you disappointed after going through all the work you have done to build out a pair of arrays, only to have a blemished final outcome.
Cheers