Start by measuring the vacuum at the main line with the Mity VAc. If the vacuum is ok at the main line with the engine running, your vacuum pump is ok. You then need to pull a vacuum on the yellow line and then the green line. Yellow is locks, green is climate control. Pull the vacuum and see if it holds. You should get an answer with those three tests because it appears the shut-off system is fine if the engine is shutting down ok.
I'd check the lines that go the Vacuum Control Valve to control the transmission on top of the IP, since if you are getting hard shifts, you have low vacuum in that system.

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1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13