I'm not aware of any quick fixes. The only thing under the dashboard to do would be to unbolt the steering shaft and replace it... I doubt that's your main problem though.
When I bought my Bullitt, it was probably about like your car, it wasn't horrible but it sure as hell wasn't a great driving car either. I went ahead and replaced every single component and bushing in the front end. What a difference it made! It drives like a brand new car!
Depending on the miles on your car, you may want to consider doing the same.
The main place that develops "slop" in the steering is the steering rack bushings. Particularly, the drivers side bushing which gets soaked with oil during every oil change.
If you crawl under the front end and look at the tie rods and ball joints, and see any cracked or broken grease boots, the parts will probably need replacing. Same goes for all of the bushings, the control arm bushings, for instance, may look fine... until the control arms are removed from the car.
Every one of those parts can cause a tiny amount of play which adds up to a little play by the time it reaches your steering wheel.