Drill holes in very tight space

If you didn't strip the holes when removing the old bolts, then you PROBABLY should be able to re-use the same holes, but to be safe, I would inject a little Elmer's wood glue (just a few drops) into each hole before you insert the bolts. This is just to reinforce the wood in the hole and help ensure it stays locked in place.

But honestly, I think you'd be wise to drill new pilot holes 1" above or below the old ones, and fill the old ones in with wood putty capped w/ a little dab of plaster (or toothpaste). The old holes will end up hidden by the mounting plate anyway, and better safe than sorry.

Using a holesaw in steel that's more than about 1/16" thick can be frustrating. The bits wear out fast, and it really likes to bind. I've had better luck using a step drill bit, like this one from Harbor Freight.