Here are some qoutes from previous owner with similiar issue like yours:
The key symptom in the discussion is that when you let off the accelerator or put the car in neutral, the vibration goes away (or in some cases, simply subsides... depending how bad your axles are).
The fact that you're experiencing this at high speeds (generally around 60mph+ sometimes disappearing at even high speeds still) and when generally only when accelerating strengthens the case for axles: really what's happen is the inner CV joint on one or both axles has failed or is on it's way out and the easy solution is to replace the entire axle.
Sometimes you'll notice by looking under the car either a torn axle boot (generally closer to the middle of the car given these symptoms) and likely grease everywhere if the boot is torn but sometimes the boot will look fine and the damage is internal. Internal damage without visible damage to the CV boots is why dealers and mechanics frequently tell you the axles are fine and continue to throw other parts at the problem but don't be fooled... I've had more then 1 CV joint fail without visible damage to the CV boot."
"CV Axles are a critical component in the Legend drivetrain. Too bad for me it took 6 years to come to this conclusion. Our cars are super sensitive to to the slightest axle vib. I must have changed 12 of them over the years before I realized my car will not drive like a Legend unless it has high quality axles installed.
I recently experienced the same vib/thumping upon acceleration at highway speed. Since yhis type of vibe is caused by the inner CV joint it is almost impossible to tell which side is shaking. If both your axles are older I reccomend replacing both at the same time to ensure a smooth ride. I am currently using Napa axles in mine. This is a "new" axle, not rebuilt for around $110. They seem to be working out good.
Also I could not visably see any damage to the bad axle but when removed it was obvious that the inner joint was trashed. Excessive play at the inner knuckle."
"Ya I have a 92 legend and I had a vibration that slowly started on acceleration at the same speed as yours and got worse about a couple weeks later it would do it at lower speeds and it only did it after i have been driving for a while but when it did start it felt like I had a square tire so I did some thinking and some simple tests and replaced my CV halfshaft axle and the vibration went away completely and my axle didn't click around corners or give any sign that it was going bad, So I think I would give that a try If I was you."
"I started this thread over a year ago. It's fixed now. It was the axles."
These are just a few comments - Here is the full thread if you want to read it...