Your pool table is absolutely STUNNING!
I've split the identification question into it's own question: Identify Model and Age of an Antique Brunswick Pool Table. There's a good chance I can ID it once I have time to dig through the archives.
Also, here's a quick diagram that discusses some of the terminology for the areas around a pool table pocket. It might help in your search for more answers and in any further communication you might have with others on the subject.
The main area of the slate in question is called the "shelf". You have a sloped shelf, instead of a flat shelf that has a 90 degree edge and a vertical wall down to the pocket.
In the meanwhile, I've asked around about the beveled pockets like the ones on the pool table you acquired. The overwhelming answer was that this was done to some pool tables to make them play easier for beginners.
Here are some of the relevant comments I received:
I've always heard that the bevel you describe was to make the table play easier. They came like that, especially on home pool tables. I've seen lots of home tables with a pretty big bevel. I think even Brunswick even did it a little on the Gold Crown (their main commercial pool table), depending on if it was purchased with real slate or "Brunstone".
About 50 years ago I was coming off a drilling rig out in the middle of nowhere Texas. I went into the local town and found a Mexican pool hall on Main Street. I got a set of balls and went to a pool table in the middle of the room and started practicing. Just a few minutes later one of the locals came over and told me I was playing on the 'ladies' table. He then showed me the beveled slate and explained it was to make things easier for beginners.
That was the first pool table I had seen with the sloped slate. Later in my travels, one of the explanations I heard for why this was done was that it made each games go more quickly in the places that charged for table time "by the rack".
Bob Jewett, a well-known contributor to Billiard Digest, owner of Bob's Billiard Books, and co-owner of the San Francisco Billiard Academy, also heard that it was done to reduce the time it took to complete each rack. This allowed proprietors to earn more income per pool table in a given amount of time.
Another contact of mine referred to them as "drop-off pockets":
A little room in my home town a Brunswick "Anniversary Centennial", and two Brunswick Anniversary pool tables . The third one had those drop off pockets. I saw it happen many times—a ball hit ever so slowly down the rail by the side could and would drop right into the pocket.
So the consensus is that this was done to make certain pool tables "play easier". Most thought your specific slate was likely ground down by someone.
The official World Pool-Billiard Association official pool table specs refer to the slate's pocket cuts as "vertical". Pool tables with a beveled shelf like yours wouldn't meet those specs (though a very slight bevel is acceptible). Strangely, they don't specify the maximum acceptible bevel radius.
Shelf: The shelf is measured from the center of the imaginary line that goes from one side of the mouth to the other – where the nose of the cushion changes direction – to the vertical cut of the slate pocket cut. Shelf includes bevel.
My thoughts are that you could probably repair that quite easily. If it were mine, I would probably make a rough mold out of a flexible material (e.g. tape a piece of sheet metal or aluminum vertically on the pocket opening), and fill it in with a product like Bondo (get it on Amazon.com). Once hard, I'd use an angle grinder to make it perfectly smooth.
There's one more contact I can pass along if you would like another opinion. Call Ken Hash at Classic Billiards in Fallston, MD at (410) 256-8388.
He's the guy to talk to for this type of stuff. He is generally always happy to help and willing to give free advice where he can etc.