Are you sure it's a 5.9? My 400 Ford $500 pickup was really a 351M as I found out when the 400's pressure plate wouldn't work on the flywheel. Later I discovered that it was a 4" stroke so it really was a 400 by means of a crank and piston swap. So it could be a 5.2 masquerading as a 5.9. That seems pretty unlikely but a lot can change in 20+ years.
It's not the ignition but the real way to find that out is to use a timing light on each spark plug lead and watch the flashes. Even at 3000rpm, a miss in the flash pattern is pretty easy to see. Once you have put the ignition to rest, everything else you said points to a fundamental balance issue.
That means it must be something attached to the crankshaft. Period.
When you wisely ran the engine without the belts and the vibration was still there, it eliminated everything that was not attached to the crankshaft at that moment.
The description of the vibration being worse through a band of rpm is right in line with descriptions of 360s with 318 converters or neutral balance flywheels.
It helps if we stop referring to a 5.9Mag motor as a 360. Magnum engines have enough different parts that even though they share bore and stroke with certain LA engines, they are not LA engines.
It is important to restate that the values for factory imbalance in 360s and 5.9Mags is different. The 5.9Mag uses a smaller amount of imbalance.
IMHO you will be removing the engine and discovering which of the several incorrect combinations you have.
