I did what you showed with the push rod. I then took the smallest precision screw driver and pushed it in with the Handel. Took seconds for it to pop into groove
What about the bleeder screw @ 6:16 with the plastic red cap on the right with the slot in it hiding under it ?, how about degreasing and rinsing all the contaminants away before they get in and chew the seals away.
Funny how your jack looks identical to mine but yet the o-ring is on the shaft and not inside the threaded casing like yours is. Frustrating part about these jacks is little repair 'kits' that have maybe 2 dollars in 5 or 6 parts companies want like $40 for the kit. Its ridiculous.