I've 'fixed' quite a number of off face SxS's with the shim the hook method.
It works just fine. I wouldn't use it on a collectible. But a shooter to bring it back to usable condition I find it a rather quick way and it holds up well.

I use steel shim stock, various thickness sheets of about 4"x6" avail as a packet. As thin as .002 and up to about .030 IIRC.
Not in .001 increments but more than enough steps in thickness to be of value.

You can kind of guesstimate what you will need as far as thickness by the bbl to face gap.
A bit too thick is Ok as you can then refit the locking mechanism for a nicer lock-up and lever position to your standards.

I attach the shim with plain soft solder. I've used lead/tin and I've used the Tin/Silver stuff.
I see no difference in performance. Neither comes apart if the soldering job is done right.

Scrape the hook clean prior to soldering. Clean the shim and I also run some grit paper over that as well to clean it.

I 'tin' the shim w/an elec soldering iron. I use plain paste flux. Nothing fancy.

I don't 'tin' the hook but I do flux it and the tinned shim once it cools off.
Then clamp the shim into place into the curve of the hook.
I use an assortment of Transfer Center Punches,,a cheap set from Harbor Freight or the like works fine.
The many different dia's usually allows you to find one just right for the job of clamping the shim nicely into the hook.
If one is very close but still needs a tiny bit of dia increase, place another piece of very thin shim stock from your supply betw the punch body and the repair shim to draw it up tight.

Cover that thinner piece of shim with pencil graphite scribble so any solder/flux doesn't solder it into place during the operation.

I place a standard C clamp from the punch back to around the bbl lug and tighten.

Soldering is best done with a torch with some pretty good heat output. I use OA
You want to get it hot fast, flow the solder and get out.

You won't loosen any ribs that way and won't disturb bluing.

You don't want to play around heating up everything around it and chance loosening especially the short underrib.
You can place an extra small clamp on that if you feel better about it.

Heat the steel not the solder joint. When you set the solder flow, add just a touch more with the wire solder and tighten clamp a bit and you are done.

Let it air cool on it's own..

Unclamp,,file off the excess shim on the sides of the lug and clean up flux, ect.

Try 'er out in the frame.
It'll likely take a bit of touch up on the locking surfaces to bring it nicely back to where you want it.

Keep the hook and pin clean and lubed

Good for another 100 yrs.