Bless you Ray C. You made me crack a book. Never hurts anyone every once in a while. I find no real inaccuracies in your statement but some terminology I am not familiar with. To my knowledge "SPLIT PHASE" is a term applied to fractional HP single phase motors and refers to the style/design of the make up of the coil winding. "SPLIT LEG" I have never run into before. Other than that I have no qualms about anything in your posts. Now "WILD LEG" is a term applied to the high voltage leg in a three phase delta supply.
As stated, true TWO PHASE is a four wire affair. Coming from two separately derived sources, the assembled in a fashion to be 180 degrees out of phase with each other. For lack of a better explanation, similar to how a DC motor operates except having a rotor instead of an armature. Consider the coils having a North and South pole orientation but changing polarity sixty times a second. This then acts upon the residual magnetism of the rotor dragging it around the stator as best as it can. I don't even know what the design speed is for a two phase motor. I suppose it is like a three phase motor and depends on the number of poles. The greater the umber of poles the slower it goes as it does not have to turn as fast to keep up with the phase (magnetism) shift generated in the coils of the windings.
Single phase is derived from a single source with a tap in the center to halve the voltage of the two phase conductors. In theory you could tap the winding at 1/3 and have 79.92v on one leg to ground and 159.84v on the other, but still 240v leg to leg. It is all a ratio deal. Think of a audio transformer with different power outputs. Same deal. One lead will put out 100% and another lead will only use 2/3 of the winding for a 1/3 reduction in volume.
On the subject of burned contacts. I would not file or burnish them unless the surface is so deformed as to hold the contact partially open when energized. That silver color, yes, it is really silver alloy so why dump it on the floor. The sooty residue will return the first time you operate the contact under load. It is a by product of arc flash cause by opening the contact under load. Once started electricity does not like to quit so until a large enough air gap between the contacts is developed, the current continues to flow. With DC, as on a ships DC open switchboard, it is very easy to draw an arc and maintain it over the air gap on an open knife switch. My first mentors used to do just that because they knew it scared the hell out of me. Ah yes, open front DC switchboards on a rocking rolling ship. Nice and sweaty down in Auxiliary Pump Room #1. Those were the days!
Just a flash but why don't we find the voltage of the motor and try to run it direct and eliminate the generator part. I bet it is just a standard motor. Thinking from a design point of view the more you deviate from standard, the more expensive the item becomes. That would never do. The engineers I used to work with would always say "Looks nice, what did it cost to do that?" After I would give them a figure they would say "Fine, now figure out how to do it for half the price."! The pictures of the control show it to be very, very old equipment that is probably do for a refresh also. Folks don't think of it but electrical components wear out too.
To be honest my man, I have tried to be real accurate to the best of my limited knowledge especially after I saw the double "E" connected to your name! On the other hand a good friend of mine is a EE for the Bonneville Power Administration and when he offered to help me trim a house he ask for terminal strips to connect the wires as he had never heard of wirenuts. Course he had not been out of school too long at the time but I still tease him about it.