How important are upper control arms?

My opinion is to leave the upper control arms alone or get rid of them entirely. This is why:

The upper control arms are for locating the rear end laterally and actually interfere (bind) in the stock suspension arrangement. The stock rubber bushings have enough compliance to allow the suspension to move and still do an OK job of locating the axle laterally. If you install upper control arms with stiffer bushings, they will cause the suspension to bind, which can cause unpredicatable handing and reduce the travel and use of the suspension. Look at the upper control arms on the MM website and you'll see the use the same rubber as the 1994-04 mustang and say there is no performance benefit to those cars using their arms.

If you can get rid of one or both upper control arms, you'll be in a much better place. You can remove one arm when you add a pan hard bar and get rid of both with a torque arm. Again, the best solution is to remove the upper control arms because they naturally induce bind as the suspension moves.

What I said above is for someone who actually cares about going around a corner. If you are only concerned with going down the quarter mile, then I guess the typical thing to do is install upper control arms with stiff bushing (bind inducing) and weld the torque boxes so you don't rip them off when the suspension binds.

Here is a picture explaination of what bhuff was saying,
Late Model Mustang Suspension Basics

The rear suspension in the 79-04 cars is definitely a case lesson on engineering compromise.

The uppers aren't solely responsible for locating the rear axle laterally: They must act along with the LCAs to generate the required triangulation to locate the axle under the car.

Similarly, the lowers aren't solely responsible for sending thrust into the chassis: The uppers and lowers both react to torque inputs (i.e. axle wind-up from both braking and accelerating forces.) Anyone who's ripped out their upper torque boxes know this. Without one or the other, the axle would obviously move sideways and/or back and forth or rotationally to an unacceptable degree.

Ideally the arms move in arcs in a single plane. But these arcs are no parallel to one another. If you start with both uppers at a given angle and measure the distance between their ends, then pivot them 20o and re-measure, you'll find the distance has changed. Ditto the LCAs. Now think about those ends: They are affixed at both ends to what amount to rigid bodies. The rear axle isn't going to deform and neither are the chassis mounts. For that matter, the arms themselves aren't going to give (at least much) either. This is what the bushings are for and it's why, for instance, from the factory the LCA fronts are elongated and squishy.

This "give" is responsible for the need for "quad shocks" which dampen the fore-aft movement of the axle allowed by those soft front bushings. It also results in a rear axle that's not all that well located. Lateral movement of the axle under the car can exceed a full inch under load, not exactly European sports car geometry...

But the give is also import to relieve some of the stress from the torque boxes. If you go super-stiff all the way around you've essentially solidified the rear axle and greatly increased the stress loads into the torque boxes. The bottoms are pretty robust but the uppers are, comparatively speaking, not. Lots of miles or harsh abuse can fatigue this metal and result in cracks forming in the brackets.

For this reason I tend to agree with bhuff: Don't try to stiffen everything in this ****ty design to the point you bind it up and risk the mounting point health. If you really, absolutely need a solid rear end then covert to a 3-link with a panhard bar (e.g. like the S197 cars) or, better, consider a torque arm arrangement which uses LCAs, a long torque arm and a panhard bar.