First off I would suggest you get the WSM for it (aka Service Manual).
P/N 97897-10835
With it in hand you will be able to troubleshoot any issue that you have with it.
Hard starting issues are more likely an issue with either the glow plugs, quality of fuel, or compression issues.
You're not "starving it for fuel" when you move the stop linkage, you're simply cutting it off, and once you let go of the linkage it returns to unobstructed fuel flow, So no, that's not the reason for the hard starting.
That model has an externally mounted stop solenoid that is controlled by a Combination box, which give it the signal to kill the motor (times it for about 5 sec).
If the Combination box is not getting power or is faulty then it won't run the stop solenoid.
Check fuses there should be 2 that control it i do believe, one low amp fuse and one high amp fuse.
I think there also might be a relay involved in this setup, but without the wiring diagram or the WSM I have no way to confirm this.
And like rentthis said, it could be just a bad stop solenoid, that's easy to test.