I have a suggestion, buy a 3/8 hardwood dowell.and a 1/4 in dowell to use where applicable. Drill those holes out and epoxy the dowell into place Then overlay with a piece of bowtuff or with a good hardwood and shoot the bow forever.
The holes are on the compression side so this should work very well and you should not have a problem with it. Oh and when you drill b e sure to tape first so you do not split the glass out.Before you put the dowels in you might go over the edges of the glass real good with very thin super glue. I use Precision Max to eliminate any glass splits or seperations. The dowell should be tight enough to have to tap it in and you will need to score it a bit for good glueing.
God bless, Steve