I think the reason you can't find his Texas death is because he didn't die in TX - he died in Mexico and was brought back to Laredo for funeral/burial.
The only thing I could find on him in 1929 newspapers is in Spanish. Prensa newspaper, San Antonio, dated Sat, Nov 30, 1929. This paper has a section for Laredo news, and that's where his death notice was. (attached)
Here's my best translation of that if you don't speak Spanish (I don't).
On the last Tuesday in the city of D. Martin, N. Leon, Mexico, the senior Martin Normandy, 26 years old, whose corpse was transferred to Laredo, Texas and deposited in the particular funeral chapel of the Funeral Agency H L Jackson.
At 4:30 in the afternoon, through the services of the aforementioned burial agency, funeral took place in the Catholic cemetery of this population."
So, he died in the city of D Martin (what the "D" stands for, I don't know), in the state of Nuevo Leon, Mexico, and was brought back to Laredo. Mexico would have his death record/certificate IF they were issuing them back then. IF there's a Catholic section of the cemetery, and he was buried in that, the local Catholic church/diocese MIGHT have some info on his death/burial. If not, then maybe the cemetery has more info.