Chris;

Do I understand this correctly?...do you mean the rod connected to to the threaded cap which has the brass ferrule and hardware, and extends down into the dashpot oil? If that has .050" (how did you measure this) of axial clearance to the bore, it sounds as though it has either worn from running dry (inspect brass ferrule for wear)...and will allow oil to bypass too easily and not give much dampening or maybe someone machined them smaller and then tried to use a more viscous oil(?)....a used but unworn replacement should be fine.

To check dashpot dampening, remove air cleaner and lift dashpot with fingertip...if there's oil (ATF) in the bore, there should be no more than about .25" of free travel before you feel dampening of motion...any more than that, could be responsible for your off-idle stumble.

Cheers