It seems like you have starter issues. I don't know how your 7.3 starter is built but some Fords have a magnetic coil on top that both engages the Bendix gear and provides the connection for the starter motor. If that coil is failing, you'll get the intermittent spins and engagements like you've stated.
Again, clamping a meter onto the starter will tell you if there is power to the starter and if it is drawing current, trying to engage.
You also need to verify that you have adequate power in the battery being used.