Totally paint them white, it's standard practice on lit cabinets and whoever shortchanged the customer should be drawn and quartered.
As far as the print goes, you can run a second on a white trans, and apply it over, you can run a second reverse printed and stick to the back, or you can run two on clear, and double layer them. For me, the choice depends on how much the customer wants to spend, and whether or not they have some sort of spec.
Also, someone left tape on the other two faces that's going to be a b*tch to remove 6 months from now...
I use arlon 4500G Clear and Arlon 3420 satin for stuff like this, no worries about edge curl since the edge is under the retainer. Save the 8518 for something that needs it...
We ended up using scraps of white reflective vinyl on the posts and we printed 3M40C mirrored for the back side of the lean panels. Worked like a charm. Thanks everyone for the great advice.