Without an explanation of which way the grain is running, I can't make an intelligent comment.
Except that you are likely overestimating the precision of the glass company cutting. For a close fit, you really can't cut the rabbet without having the glass in-hand.
I agree.
Except cutting the rabbet may not have been the best approach.
Putting four 3M Bump-ons, one in each corner will prevent the glass from creeping and there will be no accumulation of dirt in the rabbet around the glass.
You might just want to rip it down flush and get the bump-ons. They are inexpensive, about 1/2” in diameter and about 0.100” thick with a very good adhesive. The adhesive will bond with the wood. The glass naturally has a high level of friction with the resin they use in the Bump-ons. If you enlarge the image below, the package lists the actual dimensions (metric).
In my opinion, the glass should overhand the table base by at least 1/4”. It is way easier to clean glass, than to re-finish the base.
When I get home, I will measure the thickness of the glass table top I have and also the glass coffee table top I have. I will post the dimensions when I have them.
Addendum: I measured the thickness of the glass table tops I have. The store-bought table has the glass sitting on a wooden base in a cross pattern. Thickness: 0.378”. Table size: 42” round. Overhand (at 4 points): 4-1/2”.
Coffee table, shop made: 0.380” thick, 1” overhang. Resting on four 3M Bump-ons, one in each corner.
Two points worth noting: It is possible that both glass tops are the same thickness. The deviation of 0.002” thickness might be a result of poor measuring technique.
The second point, possibly of greater importance is the fact that the glass top on the coffee table has appeared to have bonded to the bumpons. That is not how they are supposed to work. I have not removed the top from the base since I built the coffee table (about 27 years ago), and I assume that the soft resin in the bumpons has bonded. The resin appears to be similar to what is used on suction cups. I will have a go at them with a razor blade when the mood overtakes me.
But the dining table top does lift off and that is only about 15 years old. Apparently I should clean both side of the glass from time to time.
My introduction to Bumpons was from my picture framing days. Two were added to the bottom corners to keep the frame from shifting against the wall and from marking the wall at the contact points.
