As you are working on the e-unit, make sure that the plunger goes up and down, and that it catches on the plastic barrel and that the barrel rotates as the plunger goes up and down when power is applied and removed. Do not oil the plunger - it's just not a good idea for long-term reliability. Make sure it works smoothly and does not bind.
The e-unit barrel can be replaced pretty easily by spreading the e-unit carefully with a small screwdriver, and that should be your next step. Be mindful of the finger contacts near the barrel - they should not be touched if possible.
If a new barrel doesn't help, you can next replace the set of finger contacts that ride on the barrel. My 681 had a finger contact that was worn away exactly where it contacted the barrel , and eventually the engine direction became erratic. A new set of fingers (there are different arrangements, so be careful) fixed the problem.
Replacing the fingers took more patience than replacing the barrel, so I would do the fingers as a step2 replacement if the barrel replacement didn't work.
After that, between the plunger operation, barrel, and contact fingers, that's about it. Good Luck.
As a general comment, I'm not a fan of spraying the e-unit with contact cleaner. It may work in the short term, but it is moving the dirt around, not removing it permanently. It would be much better to use a cotton swab with alcohol to carefully wipe down/polish the metal rings on the barrel. A little bit of elbow grease, so to speak, will be more thorough than a spray. Don't use sandpaper or anything abrasive to clean the roller either. You want it to be as smooth as possible.
Everyone probably has their own methods to handle e-unit issues, but this is what I've done and it's been successful for me and my 681 that used to be my Dad's - it still runs great.