Sounds like you are looking for "Box Framing". Where the print is Laminated on the front surface, and the sides are covered with Formica. I used to have two places in my area that did that work... the problem is that both places damaged work, and then did nothing to replace the art.
Good Luck. Hope you have better luck then I did. (I just tell people that it's not available to me any more.) (They seem happy to get the work framed when they hear how other pieces were demaged.)
LeWinter in Pittsburgh offers this service as well. They deliver in Cleveland 4x a week, as you prolly know.
Also PLAK-IT picks up and delivers locally by their rep Barbara Barlock 216-650-0335. I am 99% certain that they offer they box style you mentioned. They will give you free samples, I believe, as well.
Are you just lovin' this fabulous Cleveland weather? I am.
The “plaking” – “plaquing” “laminated mounts” or whatever you want to call it is a huge business in Canada and it originated or seems to have gotten its start in North America in Montreal, Quebec about 15 years ago. Most of the same companies doing this up here also expanded into offering canvas transfers in all shapes and sizes. It seems to be slowly expanding in the US, but it is still in its infancy compared to the amount being done in our market. Virtually every frame shop in Canada in a metro market offers the service through service centres that pick up and delivery to their store once a week.
A fellow from my area opened up in Seattle, Los Angeles and now Denver under the COLOPLAK name. They offer a wide variety of plaking styles. They do the box mount that you mentioned.
You can go to their website to look at what they offer.
Both Prolam www.prolam.com, 1-800-780-7095 and Coloplak do box mounting laminations (like a box open at the back) as well as the traditional plaques. They also do float mounts, canvas transfers and some other types of mounts.