I'm a little late to this thread, but are you doing a short run? The Gerber Edge would allow you to print reverse on clear, laminate it with a vinyl that is an opaque enough white, then put it back in the Edge and print on top of the white. You just have to source a vinyl that is opaque enough for your needs. We make an 8 mil Convex GearWrap product that is plenty opaque. And we can cut the holes off a 15" roll when you buy it. You can get it as small as a 5 or 10 yd roll.
You can use the same process with an ink jet. Depending on what you have, re-registering it after laminating the white can be a challenge. The Gerber is sprocket fed, so it's not an issue. Printing a flood of white, black or grey, then white again is probably more expensive, but if you don't have a laminator... ? How opaque does it have to be is the question.
This is one for a church printed on "Snappy" brand clear window vinyl. The white laminate isn't super opaque, but it fit the bill.
I hope that helps,
Doug Goodloe
Product Manager
Graphic Marking Systems
800-232-8018