So that was not quite the end of the journey. It turns out that the PS2 Classics and actual PS2 games use entirely separate save methods on the PS3. Copying over the .psv files placed them into the "internal memory card" that I was prompted to create when I launched a PS2 Classics game for the first time (which seems quite odd, it doesn't actually use this memory card) does not place them into PS2 classics.
On the XMB, "Saved Data Utility (PS2)" holds the actual data. The PS2 Classics saves are not stored in the PSV format, but rather in a folder with four files, including two .VME files (the one ending in 0 being the one with the actual save data). The last post on this page helped a lot, simply replace the max drive save with a .psu save created with uLaunchELF:
https://gamefaqs.gamespot.com/boards/915821-playstation-2/75185205
Basically though, using two programs called ps2classics_GUI and mymc, and roughly following the instructions in that gameFAQs post, it is indeed possible to convert from a PS2 save to a PS2 Classics save. It was very difficult to find this information, prior to searching today I had seen no mention of any of this, so hopefully this thread will serve in the future to those trying to accomplish this.
The files provided by
@zfreeman would have worked had I been using a backwards compatible PS3 and real PS2 games, but I'm on the slim so that's not an option. Thank you again for the help regardless!