Right on, DIY improvisational engineering is the oddball way!
beegar- There are obviously lots of different ways to do this. My first thought for you is to find a coupling nut sized to fit the antenna studs. A coupling nut is just a long nut with enough thread length that both studs will thread in fully from either end. You then have something similar to what IMPigpen describes with the antennas connected directly to each other.
Lacking that, below is how I'd probably approach it using the antennas you have on hand. Do you have the capability to cut a piece of metal flatstock material and drill a hole in the middle? How about drilling three holes and making a couple 90-degree bends in the bar?
Two bars, one hole each, no bending, some gluing-
Imagine a 1-1/4" or so wide by 4" long (or whatever length the collapsed of the antennas are) piece of aluminum flat-bar with a hole in the middle sized to fit over the top stud of your stand. Basically a 4" mic bar but with only the center hole in it. Make two and sandwich the telescopic antennas between them, one oriented left, the other right, one placed just in front of the center hole, one just behind it. Hold the antennas in place (hold the sandwich together) by using construction adhesive or epoxy to glue them to one or both of the bars so they won't squeeze out from between the flat-bar "bun" like a slippery pickle.
One bar, three holes, no bending, no gluing-
Use a single bar as above and plastic zip ties to mechanically secure either end of each antenna to the bar instead of using adhesive. To do so drill 3 holes in the bar instead of one, each the same diameter (sized the fit over the stand stud), each positioned on the center-line of the bar, with the additional holes located near either end of the bar. Secure each antenna to the bar by running plastic tie-wrap through the hole at one end, over the antenna, around the front or back of the bar depending on which antenna it is, and back through the hole. Do the same at the other end of the bar. Then do the same for the other antenna, passing the tie-through the same holes but wrapping the opposite direction around the other edge of the bar. Four zip ties in total, two on each antenna.
^Both those options create a more rigid, easily stand-mountable, permanent version of heathen's "opposed and duct-taped together" method.
One bar, three holes, + bending and thread tapping (or gluing)-
Make a shorter bar, with a hole in the center for the stand stud and a hole at each end sized to fit the threaded stud on the end of the antenna. Thread the smaller holes to fit the thread on the antenna studs, or drill those holes slightly large and epoxy threaded nuts to the back side of those holes. Put the bar in a vice and make a sharp 90 degree bend at end each end halfway between the holes. You now have a U shaped bar which fits over your stand stud and into which the antennas will thread. The U can open either upward or downward if there is enough clearance for the stand. Best to keep the epoxied nuts on the inside of the U as long as the studs are long enough to pass through the bar and into the nuts. That way the epoxy only keeps the nuts in place, and the nuts transfer the load to the bar. If the epoxy fails with the nuts on the outside, the antenna falls.
^Without the antennas removed (unscrewed) this arrangement stows somewhat longer than twice the length of each individual collapsed antenna. With the antennas removed it stows as three separate parts. You could probably leave the center U portion attached to the stand or your clamp.