From what I have read all good ideas to enlarge the hole.
Was wonder though, do you have pictures of both the Plate (both sides) and the shaft that goes through it ?
Not that it will change things but just to have a better idea of where you are and what approach "might" be better, pictures can talk if you let them.
Dependent on how critical the hole dimensions are and just how accurate you want the hole to be, the first idea by "gg" sounds the best and cleanest idea... to me ! Yes there is the Machine Shop, either Plasma Cut or Mill the Plate but if things aren't critical a high speed hole saw is quick and efficient.
Making a guide plate to center the hole saw, I've had similar situations and have been caught with my pants down on deciding just how to approach it and now I have a great idea for future events in that arena, thx gg !
Before this the Die Grinder, off the Compressor, worked ok, and a File works but too slow, but a hole saw that you can center on the hole with a jig... to me ingenious !
So I have no suggestions better than what was already used, and my intent of posting was more to get pictures then try to suggest another method, but I found a new way to do my own holes, wood or steel, so I click away from this thread more informed (learned something today) !
Good Luck on the Hole Project, please post up pictures on "where you started" and "where you went" !
Ltr