Help! Can't call 9-1-1. Misrouted to a time-waster.

I'm in Houston, TX and I have a landline.  We dial 3-1-1 here to reach operators who can answer questions about city services and connect callers to city departments for more details.  It used to work well but in January, it started to simply ring for 4 minutes and 15 seconds, then hang up on me every time.  I reported this to AT&T in late January but I didn't write anything down and it is still broken.  I wondered if I could call 9-1-1 since I could not call 3-1-1 so I got permission to make a test call.  It's against the law to call 9-1-1 without a real emergency so I was careful about that.  I also tested an old cell phone that has no SIM card and I don't know what generation of cell phone signal it works on.  G3 was recently removed so I wanted to see if the cell phone could reach 9-1-1.  The cell phone was able to reach 9-1-1 but the landline got a recording that said "All circuits busy.  Try again later."  I tried 13 times over 30 minutes using each of my 3 telephones and I got the same recording each time.  I don't have any trouble calling 10 digit numbers. I reported that to AT&T on January 30 and I started taking notes.  I kept trying things and I discovered that I can call 3-1-1 if I send my caller ID.  My landline is set up to block sending caller ID unless I dial *82 first.  I requested that option 30+ years ago to avoid aggressive salespeople and I have been able to call 3-1-1 and 9-1-1 before.  I think that AT&T has changed how calls are routed so that people with landlines that don't send caller ID can't call 9-1-1.  I may be able to call 9-1-1 if I send my caller ID but I have not tried that because the 9-1-1 people will not give me permission to make another test call.  AT&T has not called me to say that either problem has been fixed and I still can't call 3-1-1 so I think I still can't call 9-1-1.  I don't know if they are even working on the problem.  I am looking for AT&T customers in Houston who have a landline with caller ID blocked by default to make a test call to 3-1-1.  I know somebody with a Houston landline without caller ID block and I got her to dial *67 311 and the call went through even though that theoretically should have blocked caller ID for that one call.  So, it must only affect landlines that block caller ID by default.  If my theory is right, many customers can't call 9-1-1 when they need help and they don't know it.  The pernicious thing about what they get is that "trying again later" will just waste time.  They are never going to get emergency services.  I know that my telephone service comes from the Fairbanks central office and it is possible that it is the only central office that is misrouting 9-1-1 and 3-1-1 calls.  If you make a test call to 3-1-1 and you report what happened here and you know which central office supplies your service, please mention that.  I do not recommend calling 9-1-1 unless you have an emergency.  But I think both problems are caused by the same call routing defect.