Mostly, I think the reason your bras stretch out quickly is from having to support dense, heavy breasts. As we know, the band is supposed to do most of the work, and your bands are "working" and they're feeling it. So that's probably about 90-95% of the reason right there, IMO.
I do agree that factors such band elasticity (stretchier and/or lower quality elastics wearing out faster) and wearing very snug bands (which may be necessary for support, but wears the elastic out faster) can both play a big part. But for the second, needing a tight band for support is a function of having large, heavy breasts, so the two are tied together.
When it comes to washing, I think washing every three or so wears is a good idea, and wash if you've had a really sweaty day. For me, frequent washing means that I really don't have to do much more than soak and gently swish my bras in a mild cleaning solution (I use baby shampoo; there are lots of gentle options) then rinse really well. Gentle hand washing to me is ideal, but it may not make all that much difference as many have good results with machine washing on delicate cycle, in a lingerie bag. I see no reason to use ice cold water. Personally, I would not use hot water because heat is bad for elastic, but I fill my laundry sink (or bathroom sink, basin, what you have) with water that's around room temperature. That's not going to hurt the elastic any.
When it comes to rotation, I often wonder if rotation actually equals more total wears per bra, or only stretches out the period of time across which you can wear the bra and have it support. So, if you wear the same bra every day will you only get 50 wears out of it before it stops giving optimal support, versus 100 wears if you wear said bra every three days? Somebody needs to study this, for bra science, but there are a lot of variables that would need to be controlled for.
One thing I emphatically disagree with is that closing the bra in front and spinning it around significantly affects wear (all other things being equal).