the sync problems your experiencing is probably the issue wiimc is having as i have seen this before and it was because the video was corrupted and had audio going out of sync with the video so i had to use autogk and re-encode a new video and it was fine.

sync problems are mainly due to corrupted video and wiimc does not so far have the ability to compensate and gets stuck in a loop trying to decode and buffer asynchronously and is getting stuck due to bad video data.
but i think most players have issues compensating for corrupted video.

the encoder your using is probably buggy as hell and is corrupting your video in the process of encoding.
AutoGK is insanely old but it works to make videos wiimc loves.

i don’t have a psp so i cant help you find a encoder that would work on both

A strange thing i have seen many times is that even if all the wii’s i see are setup exactly the same with the same cios versions and so on all the homebrew behaves differently with every wii, e.g. some work perfect, some have random problems, some never work properly with any homebrew.

I hate to see someone struggling with a great home theater box but as far as i can see, it might just be an unlucky console as with my 1st release console everything works flawlessly but my neighbores console (which is also a first release) it constantly struggles to work.

I assume that less than 10% of all consoles sold fail to work properly with some or all homebrew.
I’m sorry that you had to deal with something so frustrating but of course take what i say with a grain of salt since its possible i might be mistaken about your console.