I think I see a face frame on top. You could cut a 3/8ths rabbit on the bak, maybe half an inch deep. Cut the rabbet on a table saw and keep the pieces to hold the .22 in plexiglass in place. Or if it's already assembled, cut the rabbet with a router and find some closely matching wood to cut into retainer strips and use those strips to hold the plexiglass in place.
Those narrow strips will be on the underside of the top and not very visible. Or make the strips of contrasting material and make it look like you meant to do it. Leave a little extra room around the plexiglass. Glue and then p=Pin the retainer strips in place.
Clamps: Sounds about right. First time I've run across bowclamps. Sounds like a machined cawl. Cawls are always a good idea on longer pieces, that or lots of clamps.
No T&G needed.
The more I do, the less I accomplish.