A little update...
I contacted the Museum of Flight archives, asking for information about the Ryan M-1's.
Here is the response I received.
Here’s the list of serial numbers for the 16 Ryan M-1’s built, these may or may not correspond to the tail number of the aircraft. [81, 203, 1161, 1609, 1778, 2068/2069, 2070/2073, 2532, 3252, 4281, 4327, x]. The information is from Aerofiles.com http://aerofiles.com/_ryan.html
The earliest list of aircraft registered to owners is for 1929, even though there was a federal law on the books from 1926 requiring owners register their craft, the law wasn’t really enforced until the last few years of the 1920’s. We checked the 1929 registry for Texas and couldn’t find any M-1’s at all.
We did find an Advertisement for Gray’s Flying School in the November 14, 1927 Aviation Magazine and sitting in the background is quite possibly the same aircraft as in your photos. Unfortunately the number is not visible in that photo either. There is quite a bit of information in the ad that may allow you to further your pursuit by perusing any newspapers held by the Amarillo Public Library for the years 1926/1928.
Regards
Katherine Williams
Archivist
The Museum of Flight
Here is the photo they sent me

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Zane Adams
There I was at 20,000 ft, upside down and out of ammunition.
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