I clean all greased bare metals w/ kerosene and a soft wire brush.
I've noticed that when I push up, out of first and I let the lever guide itself to neutral as I push into second it tends to jam. It seems that the "tab" on the rod that moves the "legs" inside the box slips between the legs of the R/1st lever and the legs of the 2nd/3rd lever. If I pull the lever toward me as I shift out of 1st and, once in the neutral position, let the spring pull the lever back before pushing up into second its flawless.
Shifting this way may seem a tad clunky but you get use to it and things become second nature.
If you take the box top off before removing anything else and have someone shift it so you can see whats happening, it will make complete sense. You'll also get an idea of where its jamming and what you can do to fix it. ...someone added shims to mine to push the arms closer together so the tab wouldn't slip between the leg pairs as easily. Now that its adjusted properly, it doesn't need the shims.
[edit] ...after re-reading your post it seems like your arms need to be adjusted.
Once you've cleaned, greased, reassembled, reinstalled the box and connected the column rod, reconnect the linkage to the arms and loosen the clamps. With the shift box top off you can realign the arms so the tab moves freely between the leg pairs (have a helper move the shifter back and forth in netural). Once everything is aligned, tighten the clamps and put the box top back on.
