Finally made the time to clean the seat on the valve and the 2 1/4 NORCO jack is now working great, no handle feedback anymore.
It only took a few minutes to do, thanks again everyone and specially Hiball for all the help!
The issue was that the jack would start going down when under load at the same time that the handle would come up.
I bought a long aluminum rod from Ace ($2 or $3 for that), JB weld that I had laying around and valve lapping compound (online, $6 or $7 if I recall correctly?). The ball bearing was around 25 or 50 cents at Ace as well.
I left the smaller steel ball inside the jack while cleaning the upper seat. As Hiball mentioned, you can clearly feel the “sanding” taking place while you are at it. After I felt the seat was clean enough, I turned the hydraulic unit upside down (being careful to catch the small ball bearing) and forced fluid through the valve in hopes to catch as much debris before it would reach deeper into the system.
Then I emptied the fluid completely and cleaned it up with compressed air.
Replaced the small ball bearing, then the bigger ball bearing on top and gave it a whack with a punch to form the seat. Filled up with clean hydraulic jack fluid, bleed the jack and gave it a go.
EDIT: The handle feedback persists, will try cleaning the seat again and report back.
This is what I used to clean the seat: