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I don't think the coil in a solenoid in it's last days will draw anymore significant current, they either work, or they don't. I've never had a Deuce solenoid apart, but it may be possible to open it up and tighten the outside nut while holding the bolt from the inside. Just a thought.
I can't answer the questions about starter draw and voltage drop, but clean terminals and a little Loc-Tite may cure your problems. Do you have the lock washers in place?