You certainly are not going to hurt anything fitting a new stop.Keep the old one.
Stabilizing the extractor clocking may help,if that's the problem.
Last time I bought,they were a little short on stock.I don't remember brand.IMO,any up from the bottom of the barrel will be fine.STI,Cyl and Slide,Wilson,Brown...maybe Fusion,all can make a slide stop. In my limited experience,most all of those will take minor fitting.They don't cost a whole lot,I might order a standard fit and an oversize,or just a a standard fit.
I cheat and use a Bridgeport mill when I fit one. You might want a safe edge rectangular pillar file. They do what you need.
I'd start with getting the thin flange thickness right. I use gage pins to measure the slide.You can try drill bits.Or just use corners of the slidestop to gage "enough". You can just flat lap the back side of the SS for that,measure to be sure you keep it even.
Then measure the overall width inside the slide..If your calipers say you need to take off .004,use them to be sure you take .002 off each side.
You can put the safe edge of your pillar file down on a flat surface like a machine table or piece of glass,and slide the edge of the SS on the file and the flat surface.Helps keep things square.
Do all this without the extractor.
A sharpie marker is your friend to find tight spots.You may have to tune the upper corners of the SS a bit.You don't want any edges catching the hammer on the bottom.You want it flush with the slide.
When you have the best fit you can get SS to slide,it MAY not want to slide in past the extractor.ThatsOK.Maybe even good!!. Now file the notch in the extractor to just fit the slide stop.
Then you need to learn about the small chamfer/radii on the lower inside of the extractor hook to facilitate up feed from the magazine,and setting extractor tension.
I made a copy of the Weigand extractor tensioning tool.There are lower tech ways of doing it.
Getting the extractor right is one primary key to 1911function,and its not anything that requires modifying the base,borrowed gun.Save the original parts,unmodified,so you can return it as you borrowed it.
You gain education and do no harm.
Spent brass under the extractor hook could be a short stroke .The slide is not coming back far enough for the ejector to do the job.So,would they be light handloads? A touch zippier load may help.
A 1 or2v lb lighter recoil spring may help. A tighter grip/locked wrists may help.
Question,does the slide reliably lock back on the last round? If yes,then you are probably not short stroking.If not,get a one step lighter spring.No harm to a borrowed gun.
You might look at whether the ejector is firm and stable in the frame,or loose.
If its loose,better talk with the owner.An ejector is one of those "simple little jobs" that has its pitfalls.You CAN screw up.