I'm happy to announce that I just committed support for the HiTi P520L to Gutenprint and the selphy_print backend repos. There's still some more work to be done to round out the feature set (eg the full complement of print sizes and job accounting), but it works well enough to generate properly corrected 4x6" prints.
As per tradition, I included the first successful print, and followed it up with a color chart to make sure the color correction was functional.
This was an independent implementation, using HiTi's "Open Source (All Rights Reserved)" driver, USB sniffs, and decompiled chunks of the Windows drivers as references.
Looking forward, the P525L, P720L, and P750L should work with only minimal additional effort, but their other models will require generally more work -- Despite HiTi's use of a consistent command language across most of their model line, they rely on host-supplied data tables and a lot of magic nubmers.
Consequently, additional models will require direct access to the specific printers (or at least detailed USB sniffs). Donations, hardware, and/or documentation welcome!
...onto the next bit of joy!
Update 2019/11/15: P520/P525 firmware v1.19-v1.21 fail to communicate under Linux. This affects HiTi's official drivers as well. I was able to identify the underlying problem and managed to implement a workaround.