They should have Weapon proficiency with all weapons in the spear category. Since they're otherwise limited to simple melee, this wouldn't be game breaking. I wouldn't let them wield shields since they're greater majority a two-handed weapon class. That would make up for letting them use plate (see below)
Dragoon's Heart vs. Dragoon's Claw. There is little reason why a level 1 character would choose a bonus to death saves instead of a bonus to damage. Maybe allow the dragoon a bonus to damage rolls equal to Constitution modifier instead?
Or, if you're hoping to differentiate and not just have one damage over another, you could maybe have it be a free save when hit by an effect a save could end (bonus = Con mod when save vs. death). It's on par with the Warden feature since it's only once, but immediately.
Also, this is more personal preference than hard rule. But, for skills, I'd usually try to include a set of skills for each build; so Athletics + 6 others total class skills so each build can have 3 distinct skills it uses. Maybe let the Dex Build have Acrobatics? As a heavy armor wearing class this would be a unique fit.
Finally, since it's modelling the FFTA class, why not let them wear plate without the check penalty to Jump checks (athletics)? The FFTA dragoon wears what appears to be plate armor.
