Getting rid of the factory plug in poor shape is a good idea. But I would not permanently splice the wires together. I would try to put some sort of disconnect back in place. I say this, because when I replaced the valve cover gaskets, I appreciated being able to take this plug apart and get the wiring out of the way. You will also notice most of the wiring to the top of the engine goes through this plug. So if you ever had to pull the engine, disconnect this plug and it would be much faster to get the engine out of there.Actually I just realized if I really got excited about It I could just cut that connector out completely and splice all the wires couldn't I? The connector is just there for convenience if I'm not mistaken.
I would look on Amazon or somewhere for some sort of universal wiring plug that you could retro fit. How many wires are there? A 6 or 7 wire trailer plug setup would be better than nothing.
On your power wire testing, the best way to test the heavy wiring is with two people. You have the meter and are holding it on the wire to be be tested with it set in volts, while someone else triggers the glowplugs. The voltage should drop pretty far if the glowplugs are working, usually 8 or 9 volts. Batteries are different, each truck is a little different, but if the glowplugs are working, they draw a lot of power.