We're in the same situation as you: two stops no matter what. For three of our four upcoming trips, we're overnighting in San Juan. Not great, but cheaper and we arrive in daylight. Like you, we avoid any winter connection through Chicago.

Are you flying Delta? I just checked random dates in early January and see flights that leave at 5:54 am from Des Moines and get you to EIS the same day through Atlanta and SJU. Would it be possible to go through Houston? Maybe you can call your airline and see what they can do for you.