Ellipse should work just fine (think US capitol building)—and you should be able to make it out of paper (not mache, just paper) if you make the shape right. If you’re just working in speech frequencies, you don’t need to get fancy, as long as your geometry is tight.
Getting the shape precise is going to be the hard part. My recommendation would be to draw it out large on the floor, using the two foci & string loop method. If money were no object, I’d get 4×8 sheets of 1/8” plexiglas. But a product called “lauan” will do just fine, it’s sold in 1/4” and 1/8” thicknesses from any hardware store. Should be under $20 a sheet. You should be able to have two people bend it to a pretty reasonable approximation of the ellipse, but you need the guide on the floor to make sure it’s close.
The OTHER option would be to make it out of a series of flat planes. Because of the way the ellipse works, you don’t need to have it be a continous curve (although it works better), if you break it up into small bits, you can just focus them individually.
Here’s what you do—take pieces of plywood, plastic sheet, or something like that that’s very smooth, and glue space blanket Use something like rubber cement or even elmer’s glue so you have a lot of time to get it smooth. The plates should be something like 6“x12” (doesn’t really matter, but pretty small), mount them to microphone stands (or whatever you have), at seated head height.
Arrange these on your ellipse shape on one side, and put something like a rolling chalkboard perpendicular to the line between the two foci. Put a light bulb at the foci at the seated head height. Now, focus the reflections so they make an even horizontal line across the chalkboard.
Set up the other half of the ellipse around the other foci, and have someone sit at the foci, and focus all of the reflected beams of light on their face until they can see all of them.
Now, if you swap out the light source at the other side with a person (they sit at the foci, back to back), they should be able to have a private, quiet, conversation without anyone in the middle being able to hear them.
Depending on the flatness of the boards and the care with which you arrange them, (as well as the total square footage of them) you could pretty easily beam sound from one corner of a gymansium to the other, with a basketball game going on in the middle.
I think the main trick here is to use a light source to focus your ellipse—it’s how the acoustics in opera houses (and whatnot) are tuned. Well, that and very expensive test gear.
Feel free to PM me if you have more questions, or if I wasn’t clear. It’s pretty late here, so I’m not sure if I’m making sense.