Steering wheel shimmy side to side at 45 mph

Possibly wheel bearing going out. You have replaced everything that I would normally suspect.

But there's no abnormal noise when driving. And no play in the wheel. All is tight expect for this shimmy. The shimmy does lessen when letting my foot of the accelerator at around 45-47, but still there.

Also the car shimmys side to side at 45, but not together as one when the wheel shimmys. If the wheel shakes left the car shakes right and so on.

Even though your tires are new I would be a bit suspicious of them. Try swapping them front to back to see if that changes anything.

Had tires replaced with different brand. 90% improved. Still get shimmy on rough (wavy also) pavement at any speed. Could it be wheel bearing starting to fail?

After driving for a while and feeling the shimmy pull over and try to get your hand or finger to base of hub right behind the rim. If one is warmer than the other that one will probably be your bad bearing. They tend to heat up the hub when they are going bad. Not always but some times doing this will help identify the issue. Use caution tho some times they are real hot.

Also, driving at 70 the steering is right and feels like new. When I get to 45 when the shimmy starts, it doesn't shimmy right away. If I hit some rough roads at 45, the steering wheel will eventually return.

Could it be the road surface? Pavement even on major highways sometimes becomes a bit rutted and uneven, especially if there is a lot of heavy truck traffic on it. Be sure the road you are testing on is in excellent condition. Some cars are more sensitive to this than others, and some tire profiles, even new ones are also more sensitive than others. You've been pretty thorough in covering all the bases. Sometimes there comes a point where you just have to say this is as good as it gets. It's getting to be an old car after all. Glad to hear the different tires helped so much though. Let us know if you find anything else.

The steering feels new at 70 mph on the interstate. The 45 mph is on secondary roads. I'll get the steering wheel to move left-right if I hit a recessed manhole cover with one wheel, but not shimmy if both front wheels hit a bump that is a car's width. Could it be the nature of the beast? I am thinking of replacing the whole steering and suspension due to the cars age.

I really do think that's all you can expect from a mid 90's vintage suspension/steering system. Other than ball joints, it sounds like you've already pretty well replaced everything that could wear out, judging from the list in your original post. A certain amount of deflection is to be expected from most any vehicle when hitting an irregularity in the road surface with only one wheel. As long as you have no difficulty maintaining control and the wheels return to their original position I'd say you have a properly performing suspension system. The rear suspension on these cars is also subject to wear and deterioration and can affect handling so don't forget to check rear shocks, ball joints, and the monoleaf spring. I actually got the most significant improvement in handling in my car by rebuilding the rear suspension. At that point I'd be inclined to say relax and enjoy. These are great cars and are designed for fun. I'd love to see a pic of yours.

On a different subject, where can I get weatherstripping of my convertible?

I had the car for a few days and when I drove it, the shimmy was back, big time. What causes the shimmy to be really bad after the car sitting for a week as to being hardly noticeable when driven daily in a week?

Swing and a miss. With this steering issue, could something in the rear be causing a shimmy in the steering? I don't understand how the car sits for a while and when I drive the shimmy is back, but then if I drive it continuous every day for a week or so, the shimmy is somewhat gone. I can never tell the level of shimmy I will feel. it's not consistent.

Had the car out for a drive earlier. Had the shimmy at first but improved as the drive went on. I drove about 40 mile round trip. I did notice that if the road is rough on the right shoulder, the wheel shimmys. If it's a bump the width of the car, the wheel will not shimmy. When making left turns from a stop, no shimmy. Some shimmy when turning right from a stop. I'll try the power braking on my way to work. I believe the car and steering shimmy together.

How much movement should the engine have when powerbraking in reverse and powerbraking in the drive?

I know this is a stretch and it's been 4 years but look at the motor mounts