Haste, melee procs, and canni spam on a shaman
 

I think I have a vague understanding of how proc rates and haste interact in most cases: if your proc rate is 1 per minute and you swing 10 times per minute you've got a 10% chance to proc on a given swing, but if you then stack enough haste to double your attack rate to 20 times per minute the chance for any individual swing to proc falls to 5%. Close enough so far?

As a 60 shaman, when I'm engaged in a long solo fight I'm almost constantly casting something (like Canni) while also leaving auto attack on for a quick swing in between casts, for a little extra damage and/or useful procs like Tash stick. Attack delay is almost never a factor - I don't care whether the attack is ready to go halfway through the cast or right as I finish. It just occurred to me that having any kind of haste up (spell haste, or a belt with attractive stats like RBG or Spiked Seahorse) might actually be detrimental in that situation, cutting the proc rate on individual swings while not really increasing the number of swings I'd take 95% of the time. Am I wrong on the mechanics, or should I stop lusting after a Spiked Seahorse Hide Belt?

The Wiki backs up your understanding so far. Without haste, you have a higher chance of getting a proc on a swing.

So I'd assume having no equipment haste, no spell haste, and a big slow 2hander (40-50 delay) would give you the best chance of getting a proc on a single swing.

So your question becomes: while casting/canni dancing, what does more damage - more weapon procs or more white damage melee swings? And that seems to be entirely up to what weapon you have.

The only thing I think you're missing is that the procs/minute takes into account the possibility that your weapon would have procced when it tried to swing but you were casting.

How does the formula account for that?

By activating proc chances while attack is on but not connecting them because the weapon doesn't swing.

Honestly it really feels like you can proc while casting, it just waits until right when the cast is over. Would be easy to test with a very long casting spell.

At this very moment, the strategy I'm using is to get the highest dmg and let it swing between canni's or jbbs or whatever else I'm casting.

I've found none of the proccing weapons for shaman worth it compared to poison wind censer or exquisite brawl stick.