Too often people when going for a submission get so focused on facing it that they forget all other options. This happens to me as well and I have some matches that I wish I could have changed gears.
A lot of that has to do with training and preparation, and @animalblackbelt shows an alternative solution that a common submission battle from the mounted on bar. This choke from the arm bar position for sure will catch people off guard.
Check it out below: