As John pointed out, you're going to need some way to secure the rear axle to the frame/body of the car. Right now, the torque tube is doing that for you and the strut rods are just there to keep the tube and the axle aligned. The panhard prevents side-to-side movement, something required by the switch from leaf springs to coils. If you secured new strut rods to the body, you would have to use a Heim joint or something that would not only allow some rotational flexibility, but some side-to-side compliance as well. Otherwise you'll induce suspension bind which can cause spooky handling characteristics.
Here's the most basic suspension: leaf springs are used to align and locate the rear axle:

I think you would have to devise some kind of 3- or 4-link suspension to do an open driveshaft on one of these cars. Not only do you have to keep the rear axle following the rest of the car, but you have to keep it from rotating as the wheels try to turn it along the axis of the axles themselves. A u-joint won't do this at all and will fail the moment you put the car back on the ground. The upper control arms in a 3- or 4- link are designed to do just this, as well as to help keep the axle aligned behind the car. The panhard may or may not be required depending on which setup you use. But again, the more links you have, the more bind you're going to get and the more noise you're going to transmit to the body.
Here's a 3-link and a 4-link setup. You can see how they control both lateral (4-link) and forward location (both 3 and 4-links). The 3-link needs a Panhard rod.
4-link:

3-link:

The protective sleeve that John mentions on the NASCAR is called a torque arm, and pretty much does what the torque tube does--it keeps the transmission and rear end rigidly aligned and prevents the axle housing from rotating. It is either bolted directly to the rear of the transmission or to a bracket mounted near the transmission. In fact, the rotation of the axle under power transmits the rotational torque forward, helping to plant the rear tires even harder by moving the weight transfer point. It eliminates the need for upper control arms of any kind, but still requires lower control arms and a Panhard to function effectively. Late-model Camaros used torque arms & panhard rods in their rear suspension arrangements. Interestingly, the C5 Corvette switched back to a torque tube after having an open driveshaft with a rigid "sleeve" connecting the transmission & differential (which was possible because the IRS diff was mounted to the chassis, not live).
In the photo below, the two horizontal links that connect at the center of the differential cover are taking the place of a panhard, and are called a Watts linkage. You can see how the torque arm goes forward to a bracket near the transmission, as well as the two control arms that keep the axle following the body.
Torque arm:

I think getting an open driveshaft between the transmission and the rear axle would be easy. It's the suspension that would give you headaches. If you want to change just the driveshaft, I'd figure out a way to install a torque arm near the back of the transmission and the front of the differential housing, attach the strut rods to it, and leave everything else alone. Don't attach the torque arm to the transmission itself, however, because you're technically eliminating the universal joint from the rigid part of that assembly, even though you'll have one in the driveshaft on both ends. Attaching it directly to the transmission will break the transmission case as soon as the axle moves up or down. Does that make sense?
Hope this helps.