Too late to edit, so I have to do a new post to try to actually answer your question, which I somehow neglected to do in my long winded explanation.
To figure the length, I wouldn't even do much measuring. If you can get to a table that is the size you need to fit, and you know how much fabric will be folded under it (allowing extra for the thickness of the table), place a piece of the elastic around the circle about that far in from the edge, holding it in place here and there with rocks or pattern weights. You'll only need to cut it a little bit shorter to give it enough tug to hold the fabric in place. If it's too short or the table cover has too much going underneath, it may be difficult to put them on the table. Definitely try one before you do the rest. Write down how much elastic you cut for the first one, and if all goes well, the others will be easy to measure. Don't be afraid to experiment because elastic isn't terribly expensive and wide, long zigzag stitches aren't too hard to remove. Unless you happened to find a pattern for something like this, I'm afraid a bit of trial and error is part of the plan.
Good luck! PS I think you're a saint. Is this for a wedding? Will they be used only once?!