How thick was the veneer? And what did you cut it with?
If you want to do something like this I have one other thought. Use a lot of clamps and use better glue than Elmers wood glue. I used good glue but I only have 6 clamps. I'd use a dozen if I had them. An old cabinet maker told me that I should start buying clamps and keep buying them until I think I must have too many wood clamps at which point I should buy one more clamp. He was right.
1/8 inch. Cut with a jig saw bearing a brand new blade. I cut it a little more than an 1/8 of an inch larger than the table to avoid splintered edges but the cut turned out very smooth. There was a lot of sanding involved but I have an old electric sander. It was a very clean looking well glued piece of ply. There is a lumber yard that specializes in hardwood plywood close to the house. The prices and quality are way better than I've seen other places. Really wish I'd used oak now.
Did you also use a strip to resurface the edge? I might do the same thing to a dining room table I have.