Some ideas for balancing Bladesworn's sustain:
Add a 20 second cooldown to Thick Skin (Defense Traitline minor adept) in competitive modes to reduce its uptime on Protection. This way it won't affect other Warrior specs running Defense, and only hits Bladesworn since it gets many more procs of it due to Combat Stimulant being an ammo skill (and due to Tactical Reload).
Change Shield Master's interaction with Aegis. Right now, it reflects all projectiles while Aegis is active. The reason why this is broken (aside from the sheer amount of projectile hate this trait alone provides Bladesworn by allowing Aegis to block and reflect far more than only 1 projectile) in comparison to its interaction with traditional blocking is because you can freely attack while Aegis is active. At the very least, you're locked into a blocking animation with things like Shield 5, Sword 5, etc.. With the amount of Aegis Bladesworn has access to, it lets them attack ranged-focused specs at will without a second thought. My recommendation would be letting Aegis reflect a single projectile when active with the Shield Master trait while also consuming it.
Dragon Trigger 3 (Reach) is currently benefitting from Burst-related traits similarly to Longbow's Scorched Earth - it only needs to be cast and it will proc traits like Berserker's Power and Adrenal Health. Change it so it needs to hit a target.
Unshakable Mountain probably didn't need the bump from a shield of ~800 to ~1000 when Bladesworn also gained access to much more potential ammo (Pistol 4 becoming an ammo skill and lowered cooldown, Gunsaber 3's ammo cooldown lowered from 10 to 8 seconds, and Tactical Reload's cooldown being lowered from 60 to 40 seconds). This should probably be lowered down to 800 again.
These are the ideas that come to mind from someone that plays a ton of Bladesworn but doesn't want the class to become unplayable if the sustain is hit. Not necessarily all of the changes would be needed, but I think shaving down multiple areas of its sustain in exchange for things like stability and better general usage of Dragon Trigger would be favorable for the health of the spec in competitive modes.