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If the plate has not been removed yet be careful, removing a bridge plate can be dicey and result in splitting the top seam of the guitar.
If you got through that part with no center seam split as to your questions yes, 3/16th" is the correct sized bit and yes also to a reamer with 5 degrees being for current Martin pins and 3 degrees for some of the commercially available unslotted pins since you mentioned that you want to slot the bridge and plate in the new iteration of this instrument.
Thickness varies with builder philosophy, I make my plates about .090" thick, others for thicker.
Great job!
I'm a fan of unslotted pins having been read a study that David Collins did about slotted vs. unslotted pins.
Slotted pins came into our lives with the invention of plastics. F*ctories saw it as an opportunity to eliminate the semi-skilled production operation of slotting the bridge, top, and bridge plate for unslotted pin use.
It was a cost cutting measure but what resulted was the fact that slotted pins permit the string ball to bear on the edges of the pin holes on the bridge plate. As such and over time the string balls wear away the bridge plate and eventually try to migrate up through the pin holes. When this happens you can replace or cap the plate but it's also a great time to consider converting the instrument to unslotted pins.
We have examples of guitars in our shop including a slightly pre-war Martin (1870's) where unslotted pins were used and the bridge plate still looks like new.
For unslottted pins I like 3 degree pins although they can be very hard to find and we at times have to make our own. Less taper simply permits the pin to be in contact with the plate, top, and bridge in more areas than a 5 degree pin. It's a "nit" I know and not likely to make any difference at all in the long run. And I won't get into that famous quote about in the long run either....;)
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