Replacement top for Nelson swag leg base?  

I don't think they will
... sell you just a top. But I could be wrong. I guess you could try to replicate it, though that might be a little more difficult than it looks. You'd want to be sure to get the right bevel as well as the veneer on the edge. However, the top is just particle board with laminate.
Depending on what you paid for the base, I'd consider watching eBay for a table that has a worn or damaged base (but a good top) that can be bought inexpensively.
What size/ color do you want?

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I first saw one of these tops close up about 8 years ago and was pretty apalled, its seems such a strange constrast between the elegant and robust casting and the top. Unless of course you like exposed particle board.
The bevel would be easy to achieve on a lathe, if it was mine I'd turn up a nice figured top in something dark, walnut isn't common here but it would look nice I think.
By the way aren't these the pedesta tables? I thought the swag refered to the bent tapered tube bases.

I don't necessarily feel the need to replicate the top exactly
as originally designed, I simply want to make use of the base by affixing a round top of some sort.
How big? Oh, 16"-18" offhand.
My real problem is, I don't know what the underside of the original tabletop looks like-- i.e. how it's affixed to the base. It's threaded, I suppose.
The base was a NYC curb find, unless I can concoct a top and put this thing to use, I may just set it free again.

Well set it free to me then! ...
Well set it free to me then! I would personally hold onto it until a top pops up.