go ahead drill out the old holes, then do this.

thru drill holes to the size of a dowel such as 1/2 inch or 3.8
whatever.

Cut dowel to length of the hole. plus a little bit., if room about 1.4
inch or more.

Glue dowel piece in hole. Use a hard wood dowel from HD.

Now using a dril stop on your bit, drill out the center of the dowel
but dont goto the end, set the drill stop so it drill but not thru the
dowel, give yourself some leeway like 1/4 inch.

Now your holes are pluged with a bottom and you can fill wiith epoxy,
whatever.