The Legend of Heroes: Trails of Cold Steel [BLUS31572]

I really don't understand the QT or pre QT bits, but if you mean this as the pre QT then yeah. There are black bits that cover the screen and random freezing. Sometimes the sound disappears which is then followed by freezing.
https://ci.appveyor.com/project/kd-11/rp.../artifacts

For the latest build, I can get past the Falcom screen, but it needs a handful of restarts, which is tremendously annoying. It freezes when I save sometimes too but luckily the file always gets saved.

Now, is there really a version so far that can eliminate the problems? The latest version IS more stable but the trial and errors in restarting is just unbearable. Plus the game losing sound is totally disadvantageous in long boss fights as freezing is guaranteed when the screen changes.

That version is too old. Its super slow.
I believe this is the latest pre-QT build im talking about
https://ci.appveyor.com/project/rpcs3/rp.../artifacts

Try this ^

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I always get this display (shown in screenshot) when accessing the quick travel menu after certain scenes or dialogues.
Occasionally, I also get loss of sound problem as mentioned in the previous posts.
I use the latest build, and it happens also on previous builds.

Does anyone experience the same thing?

Yes. Nothing you can do about the broken textures. (aside from waiting for updates of course xD)