You can, but it probably won’t work.
The logic board is not providing termination as is, a location is present in the board next to the scsi connector for a diode.
So one one should be added first.
Recap is not mandatory, except for the RIFA ones.
The drives often only need cleaning the head, new lube and replacing the plastic gear of the eject motor.
To use a scsi device, a diode should be added to the logic board.
For a 4 Mb Plus, a resistor should be removed from the LB as well...
The Zip 100 Plus requires a special cable, so will detect the communication mode through it.
To be honest, never had one of those, they are not the best.
Probably the head is dirty, main reason for that kind of behavior, or the head is not able to go back and forth
Even without changing the ROM the 1.44 drive is able to read a 800k disk fine.
Well, the original manual for the Apple II is showing also the 6502 upside-down.
Concerning the characters, the label on that Rom can be a clue that an upgrade has been done.
Yes, you have an original board there, not a clone.
The PSU should also be the original one, on clone units the connector was not this one.
Concerning 74LS367, yes correct part, still available.
The Apple II only needs the first ram row to work, si you can try removing the second one and...
Not easy to help without knowing exactly what clone you have. (Il or IIe ?)
Can you make some pictures of the board ? Some clones were pretty similar to the original while others were different.