Is the Nikon [80-200/2.8] a solid... lens for this use-case...?

I haven't used it, but would expect it to perform similarly to other 80-200/2.8 lenses. Manufacturers tend to put effort into making their 70-200/2.8 (and similar) lenses reasonably good. The lens you're considering is also not a third-party lens, so should perform well. However...

Vibrations from the floor could be minimised with a better tripod or strategic placement.

If you're expecting the floor to move, a tripod will not be very useful. Without image stabilization, 150-200mm would be difficult to use. Image stabilization would also allow you to reposition the camera more quickly than when attached to a tripod. If you don't need it, you can turn it off, but you can't turn it on if you don't have it.

An FX lens will have more longevity... as skill and funds improve to full-frame the lens will still work well.

FX (full frame) and DX (APS-C) are different formats. Moving from DX to FX is not necessarily improvement. While you can use FX lenses on DX bodies, lens behavior will be different.

• With the same number of megapixels, DX bodies have higher pixel densities that are more demanding of lenses. Images taken with the FX body may appear sharper (in the center).
• The edge of imaging circles tend to be "weak", so the corners of FX images may appear poorer than DX.
• The field of view will be different, so the lens of choice will be different when using DX vs FX. This may be frustrating during a transition. Wide lenses on FX aren't that wide on DX. Long lenses on DX aren't that long on FX.

I am not sure how people know... differences between lenses... it seems to be a product of experience and experimentation.

Reviews and sample images are also helpful, but it's hard to beat hands on experience. Old 80-200/2.8 lenses aren't too expensive to try, and since they're already old, they retain their value for resale if they don't suit you.