That was something I was looking at.Something based on .22 TCM seems to me to be the way to go here. It easily outperforms the 5.7x28. You can make brass from cut-down .223 cases, even ones with split necks.
If you start with a rifle chambered for .223, you should be able to cut off the threads and re-chamber the factory barrel for the new cartridge.
Subsonic loads would be easy to produce by adapting Calhoon's Blue Dot/800-X lead bullet loads for the .223. They are easily scaled up or down and can be adapted to use non-lead bullets.
A TCM is an option.Looks like that round is very similar to the .223 short being developed in Australia, just a slight difference in case length.
With the slightly larger diameter case, it could be necked up to 6mm for some decent BC bullets, or necked down for lower bullet prices.