Rhythmic Oscillations

[PetLover]

Assistance required!
I have been experiencing a pulsing sensation in my 1962 four-door Falcon 170 cubic inches for almost one year. During that period, I had the gearbox overhauled (it is a C4 conversion), the converter replaced, the drive shaft reconstructed, and the differential refurbished. The harmonic balancer has been inspected. The drive shaft angle was adjusted to 2.4 degrees at the engine and 2.1 degrees at the differential.
While driving, I get a pulsating sensation that begins subtly at around 30 MPH and intensifies with increased speed. Accelerating causes the pulsation to intensify and become noticeably louder at seventy MPH. Upon releasing the accelerator, the pulse frequency significantly lengthens and diminishes in intensity. Engaging neutral at 70 MPH and allowing the vehicle to coast results in no tremor.

The driving shaft was completely rebuilt with a bigger tube and a new slip yoke. Nevertheless, the whole drive shaft was bigger and heavier, exacerbating the situation. I replaced it with the genuine, which exhibited just little wear on the seal region.

The vehicle has been elevated on jacks, devoid of wheels or drums. The outcomes are same.

I have also examined the driving shaft and the tail shaft for alignment.
When positioned on jacks and operating from idle to 1500 RPM, there is an absence of vibration. At 3000 RPM, a little imbalance is seen from the tail housing to the differential. I accomplished this using a broom handle supported on those components while in motion.

Does anybody have any suggestions?

[RetroGamer]

If the vehicle is in neutral at 70 mph and coasts without vibration, presuming the engine returns to idle, I would consider it to be connected to engine speed.
The coast test would likely exclude differential, driveshaft, wheels, some gearbox components, and other drivetrain elements.

I would closely examine engine vibration at certain RPMs and higher. Initially, it is essential to inspect the engine mounts and gearbox mounts.
There may be an unbalanced component rotating inside the engine.
Inspect the engine fan, since I anticipate it is the antiquated steel variant. Ensure all blades are intact. Verify the harmonic balancer. I see that you have substituted the converter. Have you substituted the flex plate?

[PetLover]

I did not substitute the flex plate. Excellent decision. The one issue with it is that I must remove the gearbox to access it. The gearbox has been removed and reinstalled several times between the Ford-o-matic and the C4, warranting a Velcro attachment.
The subsequent issue is that I am 87 years old.
That does not imply I will refrain from using it again.
I may sell it "as is". I could lose my shirt. The whole assembly is either new or refurbished, from the radiator cap to the fuel cap. I stand to lose a considerable amount.

[RetroGamer]

Do not remove the transmission prematurely, since the flex plate may be intact. I was examining many options about the vibration based on your article.
Prioritize the examination of the simpler elements first.

[PetLover]

I assure you, the last thing I want to do is remove the transmission again.
However, I have been making some tiny adjustments and engaging in much contemplation.
I believed I had effectively adjusted the drive shaft angle; but, this is a Falcon, as well as a Ford, and without disparaging Henry, my '62 Ford seems inclined to go to the next junkyard for an extended repose. To provide context, my wife refers to it as "The Falcon from Hell" despite owning it for almost thirteen years and having driven it fewer than 12,000 miles. I often engage in its repair.
Consequently, below are the actions I have undertaken since my last correspondence. Removed the drive shaft and sent it to the individual who rebuilt it for continuity assessment, since I saw some runout. Meanwhile, at the ranch, I performed some shimming and aligned the transmission, differential, and driveshaft to almost a straight line, achieving an angle of 2 degrees and 5 minutes across all three components. Following the reinstallation of the drive shaft, I took it for a test run, and the vibration was less. The sensation was perceptible only after reaching 55 MPH. At speeds of up to 70 MPH, I could alter the frequency by applying pressure and effectively eradicate it by releasing the accelerator or coasting in neutral.
After returning the drive shaft to the rebuilder due to initial inaccuracies, I opted to remove the drive shaft for a thorough inspection. I saw that some balance weights remained on the yoke side in their original positions since I sent it to him for the rebuild. I eliminated them, so also reducing the length.
The vehicle remains elevated on jacks, and I have not yet replaced the drive shaft or conducted a driving test.
I will inform you of the findings upon completion.