Regarding what you said about caching: even though with ArchiveCacheManager it's already extracted, from LaunchBox’s perspective it isn’t — it’s “attempting to extract it,” so it should show the screen (briefly at the very least -- possibly too quick for humans to see).
I hadn’t actually tested a different emulator or ROM before, but that turned out to be really helpful in narrowing this down. Based on what you said and the behavior I’m seeing, I’m now even more confident about what’s going on. It makes sense why you thought the issue was with ArchiveCacheManager, even though it actually isn’t. Let me explain.
Based off of your video, I went back to a clean install of LaunchBox 13.12, switched to PCSX2, enabled ROM extraction in the emulator settings, and ran a large ROM/ZIP file. As you described, the progress bar showed, and everything worked correctly — every time. Then I swapped the game ZIP with a small one. It doesn't matter that it wasn’t a PS2 file; what mattered was that it was small. This replicated the hanging and no-progress bar.
So from that, we can deduce that the issue occurs under these conditions: loading screens are enabled, LaunchBox is set to extract ZIPs, the archive is small, and BigBox is being used. That strongly suggests a timing issue or race condition, e.g. the extraction finishes before the load screen can render or pull output.
Now, the reason this shows up with ArchiveCacheManager is because after extracting a large game (say >40MB, depending on the system), LaunchBox uses the archive cache on subsequent launches and returns immediately, as if extraction finished instantly. This triggers the same issue that small ZIPs normally cause because they are effectively instantly extracting.
And that’s the trap: if you’re playing PS2 games and see this issue, then remove ArchiveCacheManager and test again, it’ll look like the issue goes away — because LaunchBox extracts the game every time, which takes long enough to avoid triggering the race in even the smallest actual PS2 games (probably Phantasy Star: Generation 1). Hence, your thought that it was ArchiveCacheManager with the issue. It's making necessary the conditions for the issue to show up with larger games for newer systems, but it shows up every time for the small roms.
I reported the issue to the dev(s). Ya'll can't see it yet because it's pending approval but I'm dropping the link for the future: https://feedback.launchbox.gg/p/bigbox-hangs-after-launching-small-zips-with-load-screen-enabled