I really cannot say if the fuel shut off solenoid would cause this problem.
I have some thoughts on the subject though so here is my two cents.
If the Fuel Solenoid was stuck partially open to cause the engine to starve for fuel, I would think that under load the problem would be worse because of the higher demand for fuel.
The original design of the fuel shut off solenoid produced by Cummins was flawed and has a superseded part which is an improved design.
The flaw exhibited it self by allowing the engine to continue to run after the key was turned off. The engine could be shut off by manually closing the fuel valve.
The part we are talking about is in the upper left corner of this picture.
The way it works is there are two circuits in the solenoid, a high energy circuit and a low energy circuit. when the key is turned to the start position the high energy circuit (lots of amps) is supplied with power and is used to pull the fuel valve open and over come the spring holding the valve closed.
Once the engine is running and the key is released into the run position the high energy circuit is closed and the low energy circuit is energized and used to hold the valve open.
When the key is turned off the current supplied to the solenoid is shut off and the mechanical spring on the fuel valve pulls the valve closed shutting off the engine.
I had mine replaced when the engine would not shut off. It is an "easy" job to install a new one and is something you can do if you are handy.
This is my post on the
Fuel Shut Off Solenoid
I do not have an idea what is causing you low RPM when you go into first gear. 700 RPMs when idling is certainly high enough (if anything it is too high), I do not know what the correct RPM is.
I did find this thread though
http://www.irv2.com/forums/f123/94-c...ent-61623.html