I'm sure I'm not the only person who has had this problem.  My Triad stock pack covers the QD sling stud on the left side of the stock.

Is there a clever solution to this I haven't thought of yet? Or do I need to just cut a hole in the stock pack?

If cutting a hole is the solution, what's the best way to do that to make it look decent and not damage the stock pack more than needed?

This may be a case of 'which one do you want more?'

If you must have both, then I'd try mounting the swivel, then installing the pad over it. This would negate most of the utility of the QD swivel, of course, and you'd have little choice as to the routing of your sling.

To maintain said utility, I'd think you'd have to cut a pretty big hole. It's flush, so the hole would have to be not just the size of the cup, but rather that off the swivel. If you insisted on this direction, I suppose you could mark off an area to excise and take it to a local tailor, or whomever you know to be handy with a needle and thread.

The other option you have is to install another cup yourself, elsewhere on the stock. Or a swivel stud. They sell QD cups alone, so that all you have to do is drill a hole and glue them in.

Cut a hole through the pack and put a tarp grommet there to" finish" the hole?

Install a sling stud in the bottom of the stock, between the straps.