I believe you have a Bowden cable, it would be attached to the top of the cam cover and go down to the transmission on the passenger side. There should be a plastic nut on the top side, back that nut out a few turns, it supposed to delay shifting.
Yes, too little vacuum will result in hard shifts. Is there any transmission fluid in the vac line going to the modulator? If so, replace it. Also check to see if it holds vacuum, it should, for while.
Check the kickdown switch itself, it may be hung up.

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