This is not really an answer,
but rather a report on an experiment.
After the discussion here I got very curious and wanted to compare what I would call a "yeast cake" (even though this is against the traditional definition, but the texture is more or less that of a spongy cake/quick bread) to the "same" cake made with baking powder.
To perform the comparison I divided all ingredients in two and the only difference between them was the leavening.
I tried to keep it really simple, and threw together some ingredients that I had in the house (using a simple quick-bread/muffin method).
Just so you have the feeling of what the batter was like, I will add my experimental
materials:
For each cake I used:
2 ¼ cups soy milk
¾ cup baking margarine
3 cups all-purpose flour (type 550)
2 cups raw sugar
¼ cup cornstarch
½ tsp ground vanilla pods
Then for one (A) I added:
1 ½ tsp dry yeast
2 tbsp sugar
and for the other one (B) I used:
1 tsp baking powder
½ tsp baking soda
2 tbsp cider vinegar
For both I warmed up the milk and margarine just enough that it melted and added the vanilla, then let it cool down.
For A I then added the extra 2 tbsp of sugar and the yeast, and let the yeast get activated and work for an hour - the soy milk curdled and completely separated. When I made B I added the vinegar to the milk mixture and mixed - the soy milk got thicker and curdled a little. The baking powder and baking soda I added to the dry ingredients.
After waiting for an hour for A to do its thing (of course B was ready to put in the oven instantly), I poured the milk mixture into the combined dry ingredients and gently stirred, just enough for the components to combine. I poured the batters into oiled and floured pans and baked each cake on its own in a preheated oven for 40 minutes (this is when both passed the skewer test) at 350 F.
Results:
Both cakes rose to 2.5 times the batter height/level. However, B rose more evenly, whereas A rose a bit less towards the edge of the pan. B smelled like a normal cake/quick-bread, but A filled the house with a "doughnuty" smell (the most scientific term that can be used here would probably be: super yummy). When cooled and cut, both had a really (equally) nice bouncy, fluffy, slightly crumbly spongy texture. A had a bit more and larger trapped bubbles, see figures 1 and 2.
One of my taste testers (or is it test tasters) is quite sensitive to baking powder, and said B tasted a bit too much like baking powder. Everyone agreed that A tested a bit more complex. Both cakes would probably have been better with some nuts or chocolate or fruit, but I avoided these in order to have less complex experimental conditions, to make the cakes easier to compare.
Fig. 1: Side-by-side comparison of the yeast leavened "cake" (left) and the baking powder leavened cake (right).
Fig. 2: Zoomed in image of the yeast leavened "cake" (left) and the baking powder leavened cake (right).
The experiment was performed using an electric oven as I don't have a bread machine. A comparison between this two would be interesting as well.
Best Answer
Do you weigh your flour? If not, that is the one change that you can make that will make this problem go away. Most of baking, particularly at the commercial level, is based on ratios by weight.
While there will be some minor differences in the amount of moisture in 10 ounces of flour based on the humidity, how much flour packs into a cup can vary a lot on humidity, how much you've fluffed or sifted the flour first, whether you scoop or sprinkle...you get the idea.
If you don't weigh your flour when you bake, then there are lots of possible problems that could have occurred that may or may not have had anything to do with the humidity.
The only other "seat of the pants" solution is to know your recipe so well that if you notice that there is a problem, you'll catch it early. Third rise is a little late to be adding moisture, so you would have had to have noticed the problem at the beginning.
Weighing your flour and water solves many baking problems and makes you look like a pro.
Since you are weighing, then "knowing your recipe and adjusting on the fly" seems to be the only real answer. I checked around and even Rose Levy Beranbaum says if you weigh, only minor adjustments are needed. In the situation you described I might have added a bit of water at the third rise, then let it have another rise.
Another thought is that, possibly, the air being so dry caused the tops of your rolls to dry out some, so they weren't flexible and you didn't get any oven spring. A spritz of warm water across the top of the rolls during final rise and, indeed, in the oven (I do it with my sourdough loaves, for instance) helps the bread skin to be loose enough to not inhibit the initial oven spring.