MSC75, I can't speak to the difference between Philly and Texas, I was stuck with Philly because that is where State says routine applications for my home state should go. I will say the Expedited PO Box is different one than that for routine. Hopefully, they open the mail quicker for the applications arriving at the expedited PO box.
The door to door time for expedited is actually listed as 12 weeks. They are including 6 weeks
"mailing" time, which disingenuously apparently includes the sitting-in-their-mailroom time. My application arrived in a couple days, according to the USPS signed receipt, but the total time was indeed about 6 weeks before it "arrived".
I am dubious about how effective to contacting Congresscritter's office before your application is "in process" and a locator number assigned would be. LThe constituent services staff will need that locator number to give to State to get information on your application. You can try it before, but I am not sure how well the bureaucracy will handle a request for an application that hasn't been logged in, even in response to a legislator's office. You can always contact your representative's office and see what they say.
I will say in your situation I'd contact my Representative's office as soon as I got the locator number.
You are in a tough situation, I hope it works out.