940 rebuild... should I?

My 71 Dart 340 Swinger is my daily and the current 940 will shift up ok but won't kick down on throttle stomp and I basically have to stop for it to come back down to 1st or second. During normal acceleration, 1-2 is at 20ish, 2-3 is at 40ish.

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If the KD mech is not making a difference, then this is a governor issue. Either the fly-weight is too light, or the E-clip has flipped off.
Unfortunately, it's a bit of a PITA to physically check it or change it. However you can run a hydraulic pressure test to determine if it is still functioning, and to what degree.
I've never tried it but perhaps you can see the governor thru the speed-O opening, but you would still have to take the extension off to make a change.