Hi Art,

The only brand I've ever used is Permatex Anti-Seize, the regular grey stuff that's available at Napa. According to the label it contains aluminum, copper and graphite. I've never seen it separate, but it will thicken up if the cap is left off for an extended period. It sounds like it might be time to recycle what you have and spring for some new.

A 4 once can will last me 5 or more years, which I think is better than getting a larger can that gets dirty and stiffer over time. I know there are other types but I've never felt I needed anything more.

I don't like the brush in the top. It gets ragged and falls off sooner or later and I find a flux brush to be much easier to use.

The OP makes a good point about stainless. It galls and welds together easily because of it's miniscule oxide layer, and it requires some lubricant if torqued.
The zinc on galvanized bolts is self lubricating so they don't gall, but the zinc oxide that forms between the threads is tenacious and can be avoided with with never seize.

Where I live, lug nuts and caliper bolts are in a place that's wet and sometimes salty for half the year. These things may come on and off dozens of times over the life of these cars, and each time they do some metal is lost due to corrosion if they're put in dry. Unless the plan to to replace them, I think it's safer to have good threads with never seize, than degraded ones without.

Peter