The driveshaft will rotate at between 3 and 4 times the RPM of the car's wheels. At 60MPH driveshaft vibration will be around 3000 RPM which will give more of a low frequency buzz than a "shake". The wheels will be rotating at about 840 RPM. You should be able to tell the difference.

Another vibration source can be loose or worn front suspension components, such as ball joints, inner and outer tie rods, worn control arm bushings and so on.

I'm betting on a tire/wheel or suspension issue.
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Bob: Son's XC70, my 83 244DL, 89 745 (Chev LT-1 V8), 98 S90 (recently sold) and 2010 XC60. Also '77 MGB and four old motorcycles

It's not your driveshaft... I'd put money on that...or you will if you go that route. PS: There is no "weight" on the differntial and that could never cause this. The diff case just sits there it dosen't spin at speed. (find another mechanic).

Put the trans in 1st or 2nd rather than drive and see if the vibration comes on as the engine revs up to 2500-3000RPM as you drive along. Doing this in a low gear, you will be turning the driveshaft through the same ramp-up of revolutions it would go through if you had it in Drive and it shifted up as you got to 50MPH. But you'll only be going 40 or so there would be no vibration from the wheels/tires

What you describe, vibrations in the body of the car, that starts at a certian speed and the goes away at a higher speed are wheel/tire related.

You said you got new tires and then sometime after the vibration started...I"ll bet that one or more of the tires is defective. Something like the steel belts are starting to separate inside the tread. What brand tires, what quality, that's where I'd look....

If not that. Then you may have a more serious problem with the wheel bearings/hubs.

After all this work to balance the driveshaft, new transmission support member, motor mounts, and such, and such, could the balancing have failed as a balance weight welded to the drive shaft as part of the balancing, dislodged?

I'm unsure what differential you have, yet it looks the same, in those images, as the housing on my 1990 240 DL wagon and my 1991 240 sedan. Both are open diffs. Nothing special. At least your diff is not leaking fluid.

Also, there are no balance weights on the differential exterior. I do not know what you are showing us in your differential images.

You replaced the wheels when you purchased new tires? What sort of wheels do you have, then? The 14" steel wheels or something else? What make, model, and size of tire? How old are the tires? Did the tire or wheel store inspect the wheels as straight and true? Though when you installed these wheels and tires, you had no vibration.

This 55 mph vibration started after you had all this work done and bought these wheels and tires. Sometime after, you say.

Have you hit a curb or a pot hole with these tires at any time? A tire can fail in wondrous ways and the eye cannot detect a tread bulge as in a broken belt in the tire. If you have Michelin tires, doubtful. Yet if you cheapie tires, well, maybe. Though a good tire store would detect malformation, fi they can be trusted. And you had the wheel-tire assemblies rebalanced.

As you reside in the SF Bay Area, as trichard suggests, you could try a replacement drievshaft, if that is the cause of the unbalance and vibration. The Bay Area is full of junkyards. You may find a drop in replacement driveshaft from around the same year and model with same transmission. It may need new u-joints or not.

Mind you, the suggestions you receive here are for folks that could remove and replace a drive shaft your self. At 100-150+$ auto service labor rate in The City, well, I'd guess you've spent a good deal of $$$.

If you could find a set of wheels and tires that are known good you could swap from the known good 240, like someone's winter tire set they use to go to Kirkwood, and on to your 240, and drive it, that can eliminate one cause. Else, unless a brickboard member in SF could help you, you may be at the mechanic's service mercy and billing.

Also, you say when you balanced the wheel-tire assemblies recently, the tires were swapped back to front, as in a rotation, and the vibration got worse, you say.

Other than this, does your AW-7x auto transmission leak fluid at all? The tail shaft bushing could have play in it, and such play can manifest as driveline vibration.

Even with faulty front suspension bushes, like strut mounts and rear (large) control arm bushes, with well balanced wheels, there would be no vibration. Just pitching and swaying from hard turns, stops, starts, and road imperfections.

Any sounds, like moaning or groaning or growling you can hear through the speed range? Front wheel hub bearings with too much play or out of grease. The rear wheel hubs last a long time, yet should be serviced.

Your brake fluid is clean; a clear beige fluid to a light tan. Or is it black? Have any brake work done of late? Any added vibration when you apply the brakes? Do you smell or sense a wheel hub hotter then others.

Though it does not sound like a U-joint, could on of the U-joint installs be defective? A check for play can tell.

This is all speculative.

I can reach out with long arms and a 120-pound tool box to help you. If I lived in the city, I'd be by as soon as I could to help.

I guess CRO Volvo in the San Rafael Canal would be no cheaper. Yet I'd trust Carlo and his team.

https://www.brickboard.com/SHOPS/

I'd imagine you mechanic service would at least diagnose it. Yet differential weight or counter balance? No such thing on the exterior, AFAIK.

My best to the Marin Headlands and the Mt. Tam Amphitheater. Stinson Beach. Pt. Reyes. Marin Brewing Company. Marin Comm College Kenfield Campus. Woodacre. And all the Marin County Hot Tubs. Dammit.

Questions?

Hope that helps.

KGV - Used to reside in Marin County, 30 years ago this August 2017. Dammit.