I own a 2004 Freestar. At 45 mph on occasion the van will start vibrating/shaking a bit what appears to be up front. If I let up on gas shake stops. It does not occur all the time, and actually more often with AC on.
I look underneath and see no issues. Belts look good. From what I can tell engine mounts ok. I had the transmission recall done a few years ago (torque converter) and I did google this and the search indicate that when torque converter in tranny starts to go it can shake at speeds of 45mph. I was thinking
maybe the recall repair issue may have returned but could easily be something else. It does not shake under 45 mph. Also, a small clicking noise occurs just before the shaking and sounds like tranny shifting? I am thinking about calling the dealer. If it is a major repair likely will not do it and get another vehicle.
But if a few hundred bucks different story. My major concern though is safety
issue as I had an old Dodge Caravan way back where the front end went on the road, was able to pull over but van was too far gone at that point to save.

 

I also read your other post. I would start with the easy stuff. I would do a straight rotate of the tires front to rear and rear to front to see if the vibration moves. It may be as simple as a busted/shifted belt throwing the tire out of round that shows up as a vibration as your speed increases. Low profile tires just hate holes as they have little sidewall give, so something else has to give. That's why I run a taller tire on my Freestar (P235/70R16).

The other thing you can try is to put the front up on jack stands and run your tire speed up to the 45MPH range and see if the left and right side is steady or one side is jumping up and down, or you see anything out of the ordinary with the roundness of the front tires.