If you're sure there is no air, and the fluid looks good and has never been ran low, there are additives you can put in the oil that can help with noise. I've had success with FR3 from hot shot's secret. It only takes a little bit due to the small fluid capacity.

Most of the time with whine I find that there is air in the system, even if the bubbles aren't visible. If the fluid is cloudy at all that could be bubbles. Once I found using power steering fluid in place of ATF fixed the problem, that was on a truck with a hydrobooster, and those systems can be finicky at times. Some systems are a nightmare to get air out of. Certain new vehicles require a vacuum pump to be used on the reservoir while bleeding. Some times you have to bleed it and let it rest for an hour or so and then do it again.

Being that you had the system open for repairs, I'd be inclined to believe it's air in the system.

Keep in mind, parts have not been made for those pumps for nearly 15-20 years. 

If you want to consider replacement, Look to Lares. They offer a Saginaw pump designed to drop into the Thompson PS pump cans and you eliminate the Thompson growl.

Lares Corporation is who I typically recommend folks talk to. They show a reman Thompson #2038, but I'd suggest calling them.

https://www.larescorp.com/Part/2038" rel="nofollow - https://www.larescorp.com/Part/2038

Also, CVF Racing makes a billet aluminum Thompson style housing if you want to clean up things or have a PS pump that has seen better days. 

https://www.cvfracing.com/billet-ford-power-steering-pump-with-reservoir/" rel="nofollow - https://www.cvfracing.com/billet-ford-power-steering-pump-with-reservoir/

Last item...May be worth while to consider doing a complete system flush. 

Basically unhook the low pressure loop, and run one hose into the reservoir off a gallon jug of clean fluid, and then run the other low pressure line that feeds back to the reservoir into a 5 gallon bucket, and cycle in fresh type F. 

Make sure Type F. Do not use "power steering fluid". Our cars need the heaver type F fluid due to the steering box design.

Type F from motorcraft has power steering fluid on the label, as that's what it's used for the majority of the time anymore. If you can't find type F, I'm pretty confident power steering fluid will work. At the end of the day it's a hydraulic system, so long as the viscosity is in the ballpark and the additives don't eat the seals and hoses, it should be fine.

Type F fluid in some early Ford steering racks(R&P) resulted in bad leaks, and some early failures. That was in Fox Mustangs mostly, so it may also be owner's poor choice of fluid brands. I stopped using ATF in the early 90's and then got a Mark VII and heard those stories. I have never had any odd issues from actual power steering fluid, though I have not yet put it in my Ranchero's. But I will soon, PS fluid is made for it, while ATF is made for transmissions(and Ford was too cheap to discover and use ATF, instead of creating a better fluid).

So type F is fine to use, but it is not better than PS fluid. Do what you want to, but please don't debate on the wrong side of a logical issue.

DIRC the Thompson PS pump fluid level gauges spec'd Type F ?