I think I would turn up an oversized pin to be a press fit into the two existing outside holes. Then I would ream the inner hole out to suit using a 3/16″ adjustable or expanding reamer. (Or possibly your fixed 3/16 reamer with a slip of paper down one side of it to make it cut oversize, but test it on some scrap first.)
I would avoid Loctite as I always manage to get it everywhere and would end up Loctiting the inner hole as well as the two outers. And I am not a fan of knurling as the grip is a very small area on the edge of the knurl lines,which can fatigue quickly in a dynamic application such as yours.
If you do, however, proceed with the 5mm drill and ream solution, as you are now aware expect the drill bit to also drill a thou or two oversized and select your drill bit accordingly. Also measure your silver steel carefully. It often comes a thou or so undersize from nominal.
It can help to get a drill bit to drill on size if you very slightly round off the outer corners where the two cutting edges meet the flutes with an oilstone. Try drilling a hole in some scrap first to check though. Drill the hole first with a pilot drill, then with the next smallest drill bit than final size that you can get, so the final drill is removing absolute minimum metal,just a few thou etc. and acting more like a reamer than a drill.