My first, second , and third choice for your situation is the same
.... Nikon CF objectives. They are excellent and can be found in (very good) Plan Achromat types as well as Plan Apo types (not cheap!). These are finite type, 160mm tube length, and 45mm parfocal (DIN). They do not require chromatically corrective eyepieces.
You can find a brochure of what I believe was the last incarnation (before the change to "infinity") of this type objective here. It is dated February 1989:
http://www.krebsmicro.com/Nikon_CF.pdf
Starting on page 10 they start breaking down the different series that were offered. They range from spectacular Plan Apos to more pedestrian ("student grade") E Achromats.
CF/CF N Plan Apochomat (superb!)
CF/CF N Plan Achromat (excellent quality plan achromats. Not all achromats are "created equal)
E Plan Achromat
Achromat
E Achromat
You can see that I have only made comments for the first two "levels". I personally have some experience with some of the ones in these categories (not all), so I am pretty confident in their performance.
The others I just don't know and won't comment because I have only used 1 or 2 over the years (E Plan Achromats). I also have absolutely no idea of the quality of the objectives you are now using, so I can't offer any solid comparison. The only thing I feel safe saying is that that the Plan Apos will be superior. The CF/CF N Plan Achromats
should be at least as good, and a good chance they will be somewhat higher quality. For the other three level I have no idea. Many of the Chinese achromats have improved a great deal, and many look good. I've seen many excellent images made with them. It does however seem pretty clear that the quality can vary considerably.
To muddy the waters a little...
Nikon came out with the CF 160mm finite series in 1976. There have been a few iterations since then. Unfortunately they did not mark the vast majority of these objectives with the "CF" designation. And the barrel style has changed at they updated the series. So the only way to recognize these objectives is via the barrel style. The brochure I linked above shows the last version. The barrel style is pretty distinctive. Previous versions are worth consideration as well, but I have never been able to tack down a brochure for the earlier "CF" objectives. If you look for brochures and manuals for the microscopes of that time (Labophot, Optiphot) you can get an idea of what some look like. (Prior to 1976 the Nikon objectives were for the S-series microscopes, and they did requite corrective eyepiece and photoeyepieces). For example look through this brochure:
http://earth2geologists.net/Microscopes ... ochure.pdf
Be forewarned... it you go searching on Ebay you will be stunned and confused by the number of Nikon objectives that are on there, and most are not what you want! I did a quick Ebay search for the 20X. As expected prices are all over the place, but found some nice looking (latest versions) CF Plan Apos in the $550-$600 range and CF Plan Achromats in the $165 to $200 range). That should give a little idea of what the expense involved would be.
BTW, Zeiss 160mm finites should be used with their corrective eyepieces.