This won't be the best way for preserving it, but if you don't sew, this no sew method might work...there is a iron on tape type product. You can take your backhand affix to the cross stitch with the iron on tape. You then can glue some type of ribbon/cording/braid on the fabric to cover the raw edge.

If you can sew simp!e things, you can take your backing and lay it face to face on the cross stitching (pretty side to pretty side). Then stitch completely around three sides. The fourth side stitch most of the way, leaving a couple inches. Turn the sandwich right side out. You will need to hand stitch the couple inches that was left open for turning.

Good morning sr. I do lots of wall hangs in different shapes and sizes but never big ones. Two of my favourite methods are using bell pull brackets and my straw and string/wool.
I use iron on interfacing (best to Goggle how to if you’ve never used it before) on all my projects to keep the shape. When you have decided what option you want.....and yours is also a good one and you have the "hangerupper that you’ve chosen your creativity comes into play.
When I use the straw and string it’s just for small bell pulls for Christmas or the grandies and I usually add pom-poms or fringes to the bottom. Leave enough space at the top for your straw to slide in. Cut it so it doesn’t show. Thread your string, wool or ribbon through the straw using a big eyed repair needle. This keeps it from buckling. Etsy has a large assortment of bell pull brackets but I can’t remember what name they use for them.
I think the tabs that you’ve planned will be great but remember the iron on interfacing. Good luck.

I've made several bookmarks and have used leftover unbleached muslin or leftover flannel to cover the back of them. I put the two right sides facing each other, sew a 1/4" seam on all sides, leaving a 2" or 3" opening. I cut each corner on an angle so when I turn it inside out, there's less bulk at the seams. After I turn it inside out, I hand stitch closed the opening and make sure the corners are square as can be.
I've also have used this method on a couple of larger pieces, adding a loop for hanging.
Just a stitcher who saw your posting.
Diana

Thanks to everyone for their helpful replies. The idea of putting the cross stitch piece and a fabric piece face to face, sewing around and then turning inside out is what I will do. I had also wondered about using the iron on stuff to cover the back stitching. Now that I know others have used both of these solutions I am all set. All I have to do is complete my cross stitching lol!

best bet fabric glue dries clear and will stiffen the picture as well good luck SIS