I see no issue here.
As a Mexican citizen, you'll use Mexican paasport to enter Mexico. Mexico doesn't even need to care about your green card or extension letter.
As a LPR with valid extension letter, you will be allowed back into the US by CBP.
The only wrinkle is whether airline will allow you to board the plane.
With GC and extension letter - they should. But occasionally issues arise, so you may need to have printout of Carrier Guide with you to prove your point to airline manager if you need to.
USCIS has no say whatsoever in all of this: they don't control Mexican authorities, airlines nor CBP. They cannot give any reassurance without knowing laws of all other countries and airline rules.