94 explorer vibration shutter drivetrain.

Hello. I have a 94 ford explorer. 182,000 miles. Original owner. Maintained very well. Problem: You can be driving down the road with your foot off the gas at any speed and no vibration. When you apply power or load the Drive train vibrates the whole car and with a very low pitched rumble. At 65 - 75 it is very noticible inside the cabin (loud) Problem started as a slipping transmision gears. That problem changed from slipping to a vibration or a shutter under load at 45 mph to 75 mph. The transmision shop did find a damaged tranny. They rebuilt it and the torque converter. Vibration continued. The balancer has been changed. The drive shaft was taken out and tested to be true and balanced. The fly wheel was checked. I used the same tranny shop at 75,000 miles for a rebuilt and I trust the shop owner but he and his mechanics are stumped. Please help. Thank you