NH,

I was thinking, if there is room on the treads, a plunge router may be a better way to "drill" those 5/8" holes. Perhaps with a coresponding angle block / wedge to the degree you need fastened to the router base...wide / long enough to allow for the attachment of the alignment pieces Chris discussed... then with some double-stick tape and / or clamps to hold said jig you're off and running.

A plunge router is more stable than a hand drill and has a built in depth-stop, etc.

But actually, what about a bit brace. You can go nice and slow this way and forget about the jig stuff....maybe cut an oversized piece of scrap at the appropriate angle to use next to the bit to guide things. Some tape on the bit for depth, etc.

Might be one of those tasks where the old fashiond way is better--if there really isn't room for a jig and clamps.

Good luck w/ the newel