Sorry. I kind of overlooked Item #3 because I didn't understand it and I was busy trying other things. I do think that whatever is down there HAS to exert enough pressure to overcome the pressure of the water in the trap. We explored the idea that the odor could come from "above" the trap - e.g., something from underneath the sink - but we could neither smell nor find anything under the sink. (I have had mold in the caulking in the countertop behind the faucets, which I removed the caulk and replaced, but the particle board was still black under that. But, again, if this were the source of the odor, how would it get in the drains and why would we not smell or see it under the counter?)
In addition, now that it is cold and the house is closed up, the odor is less. Still acrid now and then from the drains, but more likely to be stronger from the dishwasher after I use it (I'm assuming because that trap is drained dry during the process of using the dishwasher.) To me, that would assume less volatility and therefore less pressure?
Anyway, I will look for a hose that is less than 1/4" in diameter if you still think this is worth trying after hearing all that?