https://travel.state.gov/content/travel/en/us-visas/Visa-Reciprocity-and-Civil-Documents-by-Country/Burma.html
“Procedure for Obtaining: Police certificates must be obtained from the Burmese township police station of your primary residence. Only one Burmese police certificate is required. For persons residing overseas, the most practical way to obtain the certificate is through close relatives or friends still in Burma.”
IME, the U.S. State Department does not have clue how things work in Burma.
None of my then fiancee’s friends and relatives could obtain a single police certificate on her behalf, and so she traveled the country to get police certificates.
With just 11,000 people, Hlaingbwe is likely not large enough to have lawyers. Google Maps does list a law firm that is 24 mules away though, in Hpa-An.
Your fiancee might see if a lawyer in Hpa-An or Yangon can arrange to get her police certificate from Hlaingbwe.
I agree with your fiancee that the travel risk is too high. At over 400,000 people, Hpa-An, as one might expect, does have a commercial airport, and given the war, not surprisingly the airport has closed.
”Although care has been taken to ensure the accuracy, completeness and reliability of the information provided, please contact the U.S. Embassy or Consulate where you plan to apply if you believe this information is in error or if you have further questions.”
So try the lawyer in Hpa-An. The lawyer might be able to draft a letter stating that the State department is incorrect about third parties being able to obtain police certificates.