Jack the Knife - Welcome to the forum, your first post! There's a "new member introduction" sticky forum under the General forum section, if you feel like introducing yourself and your car to the group.
https://www.sl113.org/forums/index.php?topic=529.1450Pagodatastic - Attachment will be the trickiest part, because you probably don't want to screw/staple anything into the parcel shelf wood or upholstery.
If you want to go cheap and DIY, maybe buy some thick foam and cut to fit each half. Then, sacrifice an old flannel sheet to cut some covers that tuck under each shelf and somehow attach to keep the top taught over the padding. Or, don't attach and accept the best fit you can accomplish. You could also drape it over the sides from the soft top storage area and down below shelf level to protect the side walls from dog hair. (Cut a hole for the release lever!)
If you want to have something made, you still need to attach it somehow. Right? I think that's the hardest part.
Cocomat would look very nice, but not be soft and cozy.
How big is your dog? Back when my car was on the road, I used to take my pair of 20 pound White Westies (RIP) for rides and they liked to be in the back too. Same with my 450SL and current pair of Westies. I only did this with hard top or soft top in place. And, I would take out the wooden center tray because they would walk on/in it to get to the passenger seat and back. On the 450SL, the arm rest makes a nice divider. Terriers don't sit and chill much on car rides! I don't recall the dog hair sticking to the old square weave - it vacuumed up easier than in the plush carpet in the 450SL.