So do you have any additional hornet nests you would like us to poke around in? LOL,,,,I don't have a product in mind simply because I don't know enough about the table.
Useing it as you do I see no reason for the pad nor extra durable finish. Do you get white rings from sitting a glass on it? I highly prize a few of my pocessions but I tend to use them as they were built. I have firearms,furniture and hand tools passed down by family from early 20th century that still look ok. All have been used alot by everyone who owned them. The key to keeping things looking and working good is not abusing it and doing nessary maintainance. Do you know what finish is on the table now? We can help you with refinishing it if nessary but it will require a lot of elbow grease on your part so let's first be sure what you can or need to accomplish.

Can I put a couple of coats of something on top to make it more durable?

Not without totally removing what is on there, down to bare wood. If you just "put a couple of coats" on, they are guaranteed to peel, go streaky, and look really bad.

How about leaving the good-looking tablecloth on it, over the pads? Or have a glass protector top made for it?

Can I put a couple of coats of something on top to make it more durable?

-- Do not be tempted to "slap on some poly" (as some people say). Most certainly, if it's the original finish, it's lacquer. And that lacquer has probably acquired some grime over the years (and worse yet, Pledge furniture polish). Poly will have a tough time adhering to the lacquer and can in short order start peeling off. Worse, if it's got Pledge on it, it will fish-eye (crater) and have even less adhesion.

A quick and dirty way would be to do a thorough cleaning and scuff sanding, then apply some more lacquer. You can use Watco or Deft brushing lacquer. If there's any chance it's got Pledge on it, first apply a couple of light coats of shellac, preferably sprayed on. This will seal in the silicone oil in Pledge.

But a better solution is to strip and refinish. You may still need the shellac sealer coat if there's Pledge on there.

Did I mention Pledge would be a problem???

I am familiar with your issue. Table is beautiful but beauty must be covered to preserve its beauty.

Your table still looks nice, right? And only used for special occasions? So let it be naked, or mildly decorated when unused. And use a tablecloth with pads for holidays. Or even nice placemats for holidays and if it gets messed up, THEN cover it up between holidays.

I do like the concept of a sheet of glass on the top--glass is the perfect tabletop after all. It just doesn't work as well if you're putting in or removing leaves. If you aren't, and if it's not too big a table (or you can live with a seam), I think it's a good idea.

I have read that spacers are preferred to keep the glass from directly sitting on the table and would want to research that. My mother has an antique game table with glass protecting the top that is put into service for large gatherings. Her kids end up there, hiding from the older people. We somehow always manage to spill water on the edge where it gets wicked under the glass and have to lift it when she isn't looking and clean it up...another reason for some sort of spacer!

Anyway, if it's feasible, glass! It's not like it's a priceless antique. It's auntie's table that you have because it was hers and it's pretty and practical and there when you need it.

(I have my grandmother's table and while I did refinish the top because the sun had demolished its finish, I didn't refinish the leaves because they were a trashed beyond my skill level from poor storage. So it gets a cloth when the leaves are in. And lately it's become a massive gaming table between "formal" meal uses, with the unsightly leaves in, so it has a thick felt waterproof pad plus tablecloth on it all the time. But that's because it's being used, and not gently. When I get a better play area set up, I'll shrink down that table and let it be pretty again. And I'll pull out the leaves and tablecloths for company.)