International Messages not Being Delivered

[Re-posting as a THIRD TIME because AT&T marked my second post as "Private", now without any notice or solution.] 

[Re-posting because AT&T marked my previous post as "Private" with a stated intention of contacting me to solve the problem, yet they have failed to call me when it has far passed the scheduled time, falling in delivery of even this smallest promise of an attempt to get to know about the problem.] 

Three years ago this time, my AT&T wireless number suddenly started to have difficulties delivering SMS messages out to selective international mobile numbers without clear pattern. I spent about two weeks with nearly 5+ hours per day speaking to various departments of customer support, visiting local AT&T direct stores (not just authorized stores), and switching between SIM card, devices, and carriers back-and-forth. Eventually, it was found by the "Advanced Tech Support" department on the phone that there were some very particular network-level (regular customer service rep cannot see this) blocker that AT&T network had automatically induced on its connecting network with T-Mobile. Upon removal of such, my international messaging resumed working without randomly discriminating phone numbers for delivering messages. 

Now, it has happened again... Only more difficult to find whoever that is able AND willing to be helpful. 

Question: how exactly is the current best way to reach, if they still exist, "Advanced Tech Support"? 

N.B.  Some of the routine "troubleshooting" by regular tech support is actually going to mess up my mobile service (E.g. knock out LTE, knock out 4G, knock out service at all), according to tons of past experiences  

//Update 20210831 

I just tried a few hours on the phone today again and finally got through to the Advanced Tech Support who was able to see the recorded errors (no details) of my messaging in their system. However, there is an actual carrier (name not released to me) who controls the transmission of the international messages and the blocking threshold and that is the only entity who can solve this problem. The AT&T Advanced Tech Support representative called that carrier entity at three different telephone numbers without being answered...

As of now, AT&T Advanced Tech Support has sent an e-mail to said carrier (whose automatic response said, "...[will get back] soon"...), and I have no case number, direct line number, or other ways to follow-up except a hopeless waiting game... 

Perhaps FCC and FTC is the best next step in a few days. 

I do intend to keep it updated, with or without solution. As for the previous time (when it happened in Aug, 2018), a network-level blocker was eventually removed (I was not told regarding by whom), according to AT&T tech support. It was only mentioned that the blocker had been "automatically induced by AT&T but placed with T-Mobile", which sounded very strange... So, I suppose this is definitely a solvable problem in theory, but it is more a problem of getting the particular person to do it. 

//Update 20210901 

Re-posting because AT&T marked my previous post as "Private" with a stated intention of contacting me to solve the problem, yet they have failed to call me when it has far passed the scheduled time, falling in delivery of even this smallest promise of an attempt to get to know about the problem. 

//Update 20210901-2 

The aforementioned AT&T support agent eventually contacted me within the day of the originally scheduled time and established a case in the system for tech team to work on, plus a direct line number (with extension). Currently awaits follow-up. 

//Update 20210904 

Notwithstanding the attention by an attentive community specialist representative, the AT&T Tech Team, who are actually capable of doing more, has still again failed in providing with convincing efforts but only a very broad statement of absence of resolution, quoting lack of information, regardless of multiple paths of clues that I have continuously supplied and been emphasizing. AT&T system SMS notification has indicated that they have closed my UNSOLVED case. 

Meanwhile, no news from the other Advanced Tech Team and no means nor reference to follow up with them regarding the recorded errors that were seen in the system. 

Currently planning to attempt a few more times next week and then proceed to a formal complaint with both FCC and FTC.