I decided to only elevate the rear wheel. This allowed me to build a stand that only supports a single chain stay. First, I placed a PVC pipe into a metal flange with a set screw and tightened the set screw.

Then, I spent about an hour in CAD software designing an adapter that loosely fits into the top of the pipe and cups the chain stay. Here's the 3d printed result, with some unnecessary blue tape.
Finally, for added stability, I drilled the flange into some plywood (although the stand was surprisingly stable without it).

To use the stand, I place it adjacent to the non drive side chain stay, lift the rear of the trike by the cargo rack, and lower the chain stay into the adapter. Because the lever arm from the cargo rack is so long, very little lifting force is required. The adapter's rounded edges and loose fit let the trike slide into place without careful positioning.
The net cost was about $40, so I expected this to work terribly. To my surprise, the stand is both easy to use and adequately stable!
If I had to do this again, I would replace the flange and plywood with a 5 way pipe connector with a PVC pipe in each port. The result would have been cheaper, lighter, smaller, and easier to build. I would also glue some rubber in the adapter cup to increase forward/back stability.
Below is a list of store bought parts:
Flange ~$10, https://www.lowes.com/pd/SteelTek-1-1-4-in-Silver-Galvanized-Steel-Structural-Pipe-Fitting-Floor-Flange/999930954
PVC pipe, ~$3 https://www.lowes.com/pd/Charlotte-Pipe-3-4-in-dia-x-2-ft-L-480-PSI-PVC-Pipe/1002867470
Wood screws, ~$5
Plywood, ~$20, two 1/2" pieces glued together. Frankly, only one piece was necessary.
5 way pipe connector (for people who want to have an better time than I did) ~$10, https://www.lowes.com/pd/SteelTek-3-4-in-90-Degree-Silver-Galvanized-Steel-Structural-Pipe-Fitting-Cross-Tee/999931046.