A lot of what you said is correct. The airlines I have been at do not use standard alternate minimums of 600/2 or 800/2. Instead, we use Derived Alternate Minimums.

Basically, if you have one straight-in instrument approach available at your alternate, you have to add 400/1 to the minimums on the approach.

If you have 2 different straight-in approaches, using 2 different navaids, to 2 different and suitable (consider wind, braking action, slope, length, etc) runways then you can take the approach with the higher min's and add 200 & ½ to those min's.

Derived alternate minimums are not used for driftdown alternates.

This is how it is spelled out in my company's Operations Specifications and other 121 companies may vary.

There are also exemptions to these rules, such as with exemption 3585 but I'm feeling too lazy to explain it right now.