The issue may stem more from the labeling process and here are 2 quick experiments to check.

Method 1:
Place a batch of printed labels in a 125C (Moisture Bake Out) Oven for 1 hour.  This will effect a full set of the label.  The same result can be achieved with a single pass through an SMT oven (if the label will take the heat).  This completes the fuzing and drying on the ink and prevents most of the smear associated with the volatiles in the coating.
My results were as follows with 4 different media:
Laser Etch on FR4, pre-coat: Fair (95% Read Rate), post-coat: No Read
Laser Etch on a White Marking Pad:  pre-coat: Excellent (99.5+% Read Rate), post-coat: Very Good (99% Read Rate)
Polyimide Label, no cure: pre-coat: Excellent (99.5+% Read Rate), post-coat: Poor (~75% Read Rate)
Polyimide Label, cured: pre-coat: Excellent (99.5+% Read Rate), post-coat: Good (98% Read Rate)

Method 2:
Lightly coat the labels with conformal coating, scan them, then apply and coat the board.
Labels that were pre-coated scanned at about an 80-85% rate, but those that did scan, scanned at 98+% post coating.
The extra thickness of coating did not interfere with label reading in all but a few instances.

Prior performance may not be indicative of future results, but both are good starting points before you buy new scanners.