Take it from me, they can process an express replacement without AppleCare+. They can also waive the $39 fee.

I would 100% call back and politely ask for a Senior Advisor. I have ZERO doubt that they won't help you get this squared away for free. I would even ask if they could do an express replacement in which they put a hold for like $1,000 (USD) on your credit card/payment source and send you a replacement device. You then send your old device back and they remove the hold. There's normally a fee for this, but you can assuredly get this all taken care of for free as long as you're nice and ask for a one-time exception, considering the circumstances and shitty timing.

For the camera lens and around it (where dust and dirt likes to settle), I use a clean a-tip. Works wonders.

I use scotch tape (or packing tape). Not intrusive and picks up all the dust and debris. I kind of kink it in there with my fingernail, ensuring I don’t push too hard or damage anything. I don’t like using a brush or air or anything like that since it’s pushing all of the gunk back into the device.