Shaving cream on a table: good kids activity on a wet day, right?

Unfortunately it turns out our table's finish is alcohol-soluble, and spending a couple hours covered with a high-alcohol foam was not good for it:

The center leaf I made, and is polyurethane, but we decided the original portions were probably shellac.

Initially, we put plastic sheeting on it (always have extra plastic sheeting on hand!) to protect it from further damage:

I looked up how to shellac tables, bought flakes and alcohol, and mixed up some 1.5lb. I sanded the damaged finish to get it smooth, but wasn't trying to fully remove it. I did ~5 layers of shellac, letting it dry overnight between them and covering with plastic during the day so the table would still be usable.

Unfortunately, it didn't really work: each evening when I went to put on another layer a few spots of finish would come up with the plastic. And even over a month later it's not completely cured: when we put a hot dinner dish on a cork trivet, at the end of the meal there will be little bits of cork stuck to the table. It's also way less resilient to scraping and other damage than the original finish was.

At this point we're just ignoring it, but someday I'd like to fix it properly. Possibly I'll strip the whole surface and put on polyurethane? Advice?