Take heart, I think I've found your solution.
FIRST:
I would keep the factory clamp at ALL costs.
The Midway clamp is a Tac-Star, and it's a direct copy of the original Choate design.
While good, these are NOT as sturdy as the factory clamp, and these have a bad habit of moving forward under recoil, marring the finish on your barrel.
Try to tighten them down tight enough to stay put, and the screw strips.
Choate recommends putting black electrician's tape on their's to provide enough friction to hold it in place, and to prevent damaging the barrel's finish.
First time the gun barrel gets hot, the tape melts.
OPTION #ONE:
I just checked my Police gun, and the hole in the bottom of the clamp, is a perfect fit for an Uncle Mike's Push-Button sling swivel.
www.unclemikes.com/adtemplate.asp?invky=9004408&catky=1279575&subcatky1=4548842&subcatky2=2000188On my gun, the actual sling swivel actually locks into the hole in the bottom of the clamp, I don't even need the lock base.
You can buy one of these sets from Brownell's or direct from Uncle Mikes.
I'd bet that Mike's would sell you just the swivel and the base "just in case".
If for some reason the swivel didn't fit the hole, you could attach the base with a short machine screw and lock nut, and that would work just as well.
OPTION # TWO.
Another option is to buy one of the between-the-extension sling mount plates.
These fit between the extension collar and the barrel support ring.
These are available with the sling mounting on the bottom, left, or right side.
Here's a picture of one from Brownell's.
www.brownells.com/aspx/NS/store/ProductDetail.aspx?p=12519&title=REMINGTON+SLING+MOUNT&s=29821#29821This particular one is the same model that is used on the US Marshall's Witness Protection shotguns.
Here's some more numbers to look at on Brownell's:
800-100-005
100-000-525
My advice, go with the Uncle Mike's Push Button swivel.