Re-entering Germany, with transit in the US, with only a national ID card and another passport

I am a dual German and Mexican citizen, and I currently live in Germany. It appears I may need to travel to Mexico without a valid German passport and I would appreciate any information on whether I will have a hard time getting back or not.

More specifically, my previous German passport expired earlier this year, and I neglected to renew it since I was busy at the time and I had no plans to leave Europe. However, my plans changed recently, and I will travel next week to Mexico for the holidays.
As soon as the plans changed I started the renewal of the German passport, with all the speed that the express option, a fair amount of begging, and a freshly minted PhD degree (for what it's worth) could muster. However, there is a chance that the new passport will not be ready before I fly to Mexico.

The way I see it, this should in principle be fine. I have a valid Mexican passport with a valid US visa on it, and a valid German national identity card.
Both passports have identical names (modulo single vs double surname conventions) and Germany is OK with me having the two passports.

• The flight out is direct from Germany to Mexico, and I should be able to travel exclusively on the Mexican passport (except of course for outgoing German immigration, which should not be a problem with both the ID card and the old passport).
• The flight back is via the USA, on a US airline. In principle, I should be able to travel exclusively on the Mexican passport, using the visa to transit through the US, and then show both the ID card and the old passport at German entry immigration.

However, there's a few things that worry me about that scheme.

• I'm unsure how much fuss the German entry immigration will raise to the ID card. I've been able to enter that way previously; however, that was only on flights from the UK, and the person at the passport office indicated that there may be differences there. I find this unlikely but I would welcome confirmation that this is possible.
• I'm wary that the airline will deny me boarding for the flight back if they become unconvinced that I will be allowed into Germany. How likely is the airline to take the ID card as proof that they can deposit me at the far end without a problem? What about the expired passport? I can in principle enter Europe as a Mexican tourist, but that might require e.g. a later ticket back to Mexico, which I do not have.
• I'm also wary that the US will deny me entry if for whatever reason they feel I'm a stay risk. Thinking back on previous US transits, I can't remember whether they asked to see the second passport. To what extent does "this person will be able to enter wherever they're going next" figure in the logic of US border officer?

Are these real potential pitfalls, or am I simply stressing a tad too much over flying without a full set of docs? What sort of documents can I bring with me that will help smooth over any rough edges?

Edit: thanks all for your responses, they've got plenty of useful information. I've just heard from the Bürgeramt that the new passport is ready, so all of this is indeed just over-stressing.