I know where I have Portal, it's on my secondary disk. I have Wine on my pc, so I can actually run the .bat. I did use the latest .vpk and the additional files.
Ok, lets start at the start :) So you've got the xdelta, bat, and exe in the same folder as portal_pak_002.vpk. That should spit out a Media.zip, which should then contain the files you need to replace in the install/ApertureReconstructed.vpk. The MD5 on Media.zip should be 8AB4E954A0F235F61FAD46CD2152D5B3, and if we can confirm that we're know we're good up to this step :)
I guess that's progress? The MD5 is the same so the zip should be correct, but it still sounds like something is very wrong with the setup. Now that we're known good at this point it might almost pay to do a completely clean reinstall: delete everything that's on the Vita and install the 4.0 vpk, and then overwrite the Media folder with the unzipped Media.zip./
Frankly I'm impressed that you've stuck at trying to figure this out instead of bugging someone on reddit/discord for a working copy lol