Here's their supposed badge, as appeared on the group:
There are some issues that makes it un-heraldic: dark grey isn't a color traditionally found in heraldry, and there are many contrast issues (for examples, green on blue and blue on grey). So I decided to make a more heraldic version of it.
From the fourth quarter, the Texas flag was rotated and became an inescutcheon (a shield on the center of a bigger shield or part). The vertically-divided shield (said per pale in heraldic jargon) has two interesting features: each part refers to part of the club's name ("Alamo City" and "Rugby"), and their blue-white contrasts intendedly well with inescutcheon's white-red.
The first part is blue (the main color of the team) and contains the Alamo fortress, that gives the club its name, and an ox's skull, commonly featured in the symbol of the team. I like the result of this part because the Alamo, made of limestone, really has a white color, and the white skull on blue appears to be an unofficial logo of the club.
The second part has a vintage leather rugby ball (that I colored red with white details) between the green shamrocks (often represented in heraldry as trefoils), in a motif that alludes to the first quarter of current design.
I like the way that, without adding or removing elements, it's possible to transform a then totally un-heraldic device in a charming and conventional coat of arms.
Comments and suggestions are gladly welcome.
I'll probably return with flags next weeks. We had two consecutive "etc." posts.