More details of the vehicle in question would be helpful to be sure. However, from personal experience, my guess would be that the shakes are not solely due to the engine being run at high RPM.
The Mercury Grand Marquis is equipped with a 4.6L Modular V8 engine and 4R70W automatic transmission, similar to many other products of the Ford Motor Company. Notable among these, at one point or another, have been the Ford Mustang, Ford Crown Victoria, Lincoln Town Car, and the Lincoln Mark VIII.
In the Lincoln Mark VIII, 65-70 MPH in 2nd gear was very doable. In fact, redline (6,000 RPM) for 2nd gear got you going at around 90 MPH. Maintaining such a high engine speed for long durations would definitely get things heated up a bit, but it's nothing the car can't handle as long as you don't do it for too long or too often.
I once had to do this myself to take the Mark VIII for repairs after the one-way clutch had failed - rendering the transmission unable to engage any gear higher than 2nd. To get to the shop where the work was going to be done required about a half-hour or so of highway travel. Parts of the highway were 65-70 MPH zones, where of course most drivers were running 75-80+. The way I managed the trip was to take the car up to speed until the engine started to get too warm, and then coast in neutral long enough to let it cool down to a more regular temperature before engaging the transmission for another run. I definitely don't recommend doing this if it can be avoided, but it should serve as a case example for two points:
- It's doubtful that your car was redlining at 65-70 MPH in 2nd gear.
- A one-time incident of approximately 5 minutes' duration at that speed, while not exactly good for the car, should not cause significant damage to an otherwise healthy drivetrain.
Given the shaking that you've experienced though, I'd definitely want to have a professional take a look at the car.