Using the arm to help isn't completely off the table, but pretty close, largely for reasons you conjectured about in your post. First, we can't actually push while driving, because the motor controllers are shared between the arm and the wheels -- you can run one or the other, but not both at once.
We could, potentially, push down with the arm to lift Spirit slightly, then run the wheels. But Spirit's just not strong enough to make much difference. :-) In the best case, we can push down with maybe 70N of force, and that's if we had a hard surface to push on. (But if we had a hard surface to push on, we probably wouldn't be mired in this stuff in the first place.) For comparison, you'd need to apply ~ 650N to completely lift Spirit, so the arm can apply only about 1/10 of the needed force. As you can see, she wasn't designed to do one-handed push-ups. :-)
Further, doing so would pose a high risk of damage to the arm itself, and since four of Spirit's science instruments -- about 2/3 of the total science payload -- live on the end of that arm, the potential downsides are quite significant.
In addition, it's not completely clear that pushing down with the arm to partially lift Spirit would actually help: one effect of that would be to reduce the traction on the wheels, and not having enough traction is one of our big problems here.
Resculpting the terrain is a less unlikely scenario, but something we're keeping in our back pocket for now. There are few suitable rocks within reach, we've never tried it and (again) would risk damaging the arm by doing so, and on top of all that we don't even know if it would actually help, since the rocks might simply slip quickly under the wheels without moving us forward much. Even so, if things get desperate enough, we might possibly try that one.
The soil we're stuck in is very weird, and has some counterintuitive properties. It doesn't work like dirt or mud. We mixed up a batch of simulant to drive our test rover in, and while there are known differences between the simulant and the real soil, the experience of working with the simulant is quite illuminating. The stuff feels like flour and flows like water: run your hand through it, and it flows away from you like water does, it just stops moving sooner. Weird, weird stuff.