96 Crown Vic P71 Steering play/wander

I have a 96 Crown Victoria Police Interceptor. The front end feels as if it it steers itself. The steering wheel has a bit of play but nothing too significant. I have changed the tie rods, idler arm, and the upper ball joints. They were obviously worn out as I could visually see the play in these parts while someone was steering the car and I was under it. I'm considering either the pitman arm or the swaybar next. Will changing the swaybar bushings make a significant difference or should the entire swaybar be replaced? If I change the pitman arm do I need to get the front end aligned again. Incidentally, after changing the above parts I DID get an alignment done. I was also told that maybe the wheel bearings aren't adjusted properly or just worn out. Can I just pull them out and repack them, and put them back in according to the specifications? I seriously want this issue corrected as it is sometimes scary to drive the car. Is there anything I am overlooking? The one thing that I don't know how to check is the steering column and its adjustments. Is there anyone that can show me a picture of the shaft and what I should check and its specifications?
Thanks to anyone responding.

do you have a brake dragging? swap sides of your front tires and see if it pulls the opposite way if it pulls to one side. loose steering gear,worn shocks worn out control arm bushings.. the list goes on and on

Thank you for your reply fleettech. I will check the tire positions and swap them today. I really don't think it is that because the wander is not specific to a side or direction.
I don't know how or where to check the steering gear. Can you give me some insight into this? The steering gear is directly connected to the pitman arm isn't it? How do I know if it is loose? What are the specifications for it?
I've read that the universal joint, near the brake booster, can seize up, can this also be part of my problem?

The pitman arm is on the drivers side of the car on the end of the steering gearbox at the end of the steering wheel shaft. Check play at the pitman and steering gear joint by jacking up the front of the car and putting it on jack stans. Unlock the steering and from the outside of the car turn the wheels left to right while looking at the joint where it attaches to the center drag link. You should not see any play, but it should rotate freely. If there is no play then try moving the pittman arm against the gearbox by moving it with you hand. There could be internal wear to the gearbox itself which can be hard to detect. Let me know how it goes.

On the steering shaft there are one or two knuckle assemblies. You can check them by jacking up the car and unlocking the steering and trying to turn the wheels by rotating the steering shaft back and forth, if there is play you will feel it. Normally they bind up and make it stiff to turn the wheel. I have heard of the knuckle breaking, but I have never personally seen it.