Murray,
I sympathise with your problem and I have had to face this three times now with my beloved Martins, once with a Gibson and once with a Takamine.
The solution that worked for me each time is as follows:
(1) Lay the guitar down on some bubble wrap on a level surface whilst working on it, that avoids any scratches, drink a small Scotch. Ready?...
(2)Drill a very small hole about a quarter of an inch deep with a hand-held modelling drill in the inside part of the heel, that's the bit closest to your body when you are playing (neck block) where you want the button to be, masking it first with a little masking tape so the drill won't slip. Remove tape when it's done.Clean with alcohol to get the sticky stuff off.Don't ever use a power tool!!!
(3)Expand the existing drilled hole for about half it's depth with a slightly larger bore bit in the handheld drill, what we are looking for is to avoid any splitting when the retaining screw is fixed in.The hole should be slightly cone-shaped.
(4)Cut a leather washer to the same size as the strap button base, it'll need a small hole to take the screw, and then place:
   (a) the washer next to the heel stock
   (b)Then the strap button
   (c)Then the screw into position in the hole.
(5) Screw it into position very slowly and carefully. Not too much pressure at the end when the button presses against the washer - ok?
(6) Attach strap and grin, drink somewhat larger Scotch.
I really don't recommend fixing the button onto the Micarta area as it's permanently under pressure from the guitar case lid when your Martin is in the case ( think about it).
Hope I've been of assistance to you, this has always worked for me and I was shown by an expert.,
Happy New Year,
Roger Knowles