Lost BRP and US Government shutdown

Hello,

I have indefinite leave to remain in the UK (my husband is a citizen). I managed to lose my BRP right before our trip to the USA on December 18. We went anyway because the risk of me having to stay longer was better than missing my brother's wedding and likely my last chance to see my grandpa before he dies (if it had been any other trip we would have cancelled and stayed home). Given we were going to be out for 2.5 weeks we figured that would likely be enough time to get the replacement BRP visa or else I could stay an extra week if needed.

Well, I made the application on December 19 (and can I say, many of the questions were not applicable to our situation and therefore a pain to fill out). I got an appointment at the Application Support Center in Grand Rapids, MI for 24 December. We went to our appointment only to find out by a notice on the door that the office was closed due to the partial government shutdown and that they will contact me with a new appointment.

In spite of my emailing people and being told I would get contacted by someone within a couple days, I still haven't heard anything. I called UKVI this morning (January 2) hoping to get more information and the person was far from helpful. She basically said that I should email the center in New York (which I can't find any contact info for) and if I haven't heard from them then I just need to make a new application and appointment. This seems crazy to me. Also, given the US government shutdown doesn't seem to be ending anytime really soon, I'm scared I'll end up in the same situation all over again anyway.

My question(s) are:
1) Does it make sense to cancel my current application or is it better to wait it out and hope for a new appointment when the government opens up again?
2) If I would set up a new application and appointment in Chicago (biggest city I can get to easily) would they do their own biometrics or am I going to run into the same issue where appointments aren't available until the US government gets their act together?
3) How far out should I book my new flights to be on the safe side? Aer Lingus will let me rebook my flights anytime up to 2 hours before the flight takes off tomorrow night (my husband will be on the flight regardless as he has to go home to work). I really want to avoid the expense of changing my flights twice, but staying an extra month just to be on the safe side is a lot longer of a trip extension than I had hoped for when we flew out (I figured an extra week maximum).

PS: We have read other situations where people just flew and hoped for the best at the border, but we're not willing to risk that given we're flying with my 2 year old and 6 month old (just in case you're wondering).