HSS was out of the question because my tiny TT350o didn't have (anywhere near) enough power.
Did you try it withOUT the modifier? When shooting out in full sun like that, you can often use the flash bare since it is there to bring the face out of shadow but will not be powerful enough to overcome the sun and create other shadows you don't want.
And I chose the tripod over a flash stand because it had a handle for carrying and a hook beneath for adding extra weight to make it not fall over (lesson learned btw).
Ya I was going to mention that. But also females models almost always have a purse with them. Even with the light stand, you can hang their purse off the bottom knob of the stand to help weigh it down. It is always nice when the model brings the light stand weight for you. And if it has been raining or recently wet, she will appreciate you storing her bag off the ground. Win win!
I personally would start with just using reflectors before even going into a speed light of any kind. That will allow you to use the full range of shutter speeds.
Which works great if you have a helper to hold and manipulate the reflectors. When shooting all alone the flash on a stand is often easier to work solo. For working alone I vote for some ND filters and the flash setup.