I was just wondering if it's possible to specifically transfer a save file that only has the Character's build/level/and all items in general to a fresh new installed game. That means excluding the progress, old save files, and already-read text.

Is this do-able?

The save folder contains: (disregarding the .bat files, which are just backups)
1) save slot files - save###.dat,
2) read text data (probably) - rt.dat,
3) everything else, which includes NG+ transfer data (which is what you're asking about, right?) and unlocked dictionary/CG/scenes data - save.dat.

So you only need to grab the latter and leave the rest.

The "global" save (save.bat) basically stores everything that is not covered by individual save slots and read text. It's all in a single file, you can't separate it in any way.
If you transfer this save to another machine with a fresh install, it won't be "fresh" anymore, it will have the same dictionary-CG-scenes unlocked, NG+ available (if it was available before, ofc.) and transfer data.

Edit: Yes, you can start a new game+ and transfer items/characters from your last route completion, as usual.