Best of the bests

Using the word best as a noun is perfectly acceptable.

Best is a singular noun and its plural does not technically exist. Cambridge Dictionary

'Bests' is an incorrect way of spelling the word 'best'. Now, there are many who use and have commonly used the incorrect word 'bests'. However, there are various words that only have a singular form. Think of furniture, money, greed, etc... When using these words, you say "The furniture is", "Money is", "Greed is", etc...
You can mind more examples of such words here.

So in your examples, all the spellings 'bests' are all misspellings of the word 'best'. Apart from that, the nominalization of the verb 'best' is commonplace and accepted.

The phrase 'best interests' is also just that, not 'best of interests'.
Example:

I have your best interests at heart. Merriam-Webster

It is also:

Best of the best.

If you want to talk of various best achievements, it is correct to say something such as:

My best achievements in the following fields are: 1.62m (high jump), 8.91m (shot put), 27.43s (200m), ...
or
I have various best achievements which are ...

Hope this helps.