The Iron Colonel

There's a fairly easy way to determine the minimum weapon speed for a given amount of haste to ensure steady does not clip the 0.5s auto 'refresh time' (not sure the established terminology here...). Do this:
Now, I'm not sure what the server/client mechanics are so you may or may not have to double the latency and reaction time values (Tl and Tr, respectively) - someone with more knowhow can probably answer that question.

Example:
Quiver, 5/5 SS so H%=1.38
Tl=latency=100ms=0.1s
Tr=reaction=100ms=0.1s
Therefore min weapon speed to not delay auto with steady is
1.38*[(1.5/1.38)+0.1+0.1+0.5]~2.47

A couple of conceptual things to note. The partial derivatives dF/Tl=dF/Tr=H%. This isn't surprising, since those values are unmodified by haste and consequently F should only vary proportionally with H% if they are held constant. The partial derivative dF/dH%=Tl+Tr+0.5; if haste percentage is held constant, F varies proportionally with the sum of Tl, Tr, and the constant 0.5. This is all pretty much exactly what you'd expect, so the equation makes a reasonable amount of sense to me in that fashion (sorry, sometimes I need to check my own work like this).

Anyway, as you'd expect, since Tl, Tr, and the constant 0.5 are unaffected by haste, as you get more haste your min weapon speed goes up linearly. If we put the equation into a more clear line form (y=mx+b) we can see F=H%(Tl+Tr+0.5)+1.5. The slope of the line, depending on which variable is held constant, is either the haste or the sum Tl+Tr+0.5 (again, you'd expect this by looking at the partial derivatives). The y intercept is always Tl+Tr+(0.5+1.5), since H% can't be less than 1 (well, it could if you had some debuff that decreased attack speed, but I'm not gonna get into that because it's irrelevant to the conversation).

Anyway, hope that equation can answer some questions (there was a bit of confusion related to auto/steady times with haste).