replacing door handles for 1.75" hole size?

Howdy,
"How hard can it be?" I figured. Unfortunately I came to learn the hard way that the bore sizes on my/8" thick interior doors are weird in my 1970-built home:
1.75" diameter handle bore, (center of which is a 2 3/8" setback) 7/8" on the bolt bore. Door is 1 3/8" thick.
Anyone know of any inexpensive replacement handles designed to drop into these without having to drill out the existing doors?
Modern door handle sets available everywhere seemingly have a template for a 2 1/8" bore or more--and everyone considers them standard. While some of these can handle the little 7/8" size bolt bore I have, some require a full 1". The problem I have is that when inserting the bolt, it can't be inserted all teh way because the relatively small handle bore isn't big enough to allow the bolt to come all the way in. The medial of the handle bore is 3.25" from the door edge, and most bolts need 3.5" of depth to fit, even with setback adjusted for the minimum.
I wouldn't be so opposed to drilling if I knew of a tool that could easily enlarge and center an existing bore (seeing as a standard hole saw has nothing to center on).
Thoughts, aside from replacing all the doors? :-) Is there a handy hole saw designed for the duty I need here? Or would doing this require putting something temporarily in the hole to center a standard bit?
-- Todd H. http://www.toddh.net /
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Get a scrap of plywood. Measure in 2 3/8". Drill a hole with a 2 1/8" hole saw. Clamp this now drilled plywood to the door over the existing hole. Drill the 2 1/8" hole in the door using the clamped plywood to guide the hole saw.
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calhoun wrote:

That's a good suggestion. Another way is to just clamp a scrap of plywood over the door so its edge is lined up with the door edge, and then use your hole saw to drill through the plywood and the door at the same time, following the instructions that come with the hardware for setback.
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