Brace yourself and stand your ground: maybe a Dex save, maybe a Con save.
I'm not sure fire cares how hard you grit your teeth. I mean, you can still do this, but it won't save you any hp.
Basically the same thing as the default dex save to dodge. Presumably you get up as part of the dodge to avoid making this a strictly worse option than the default.
This is already in the PHB as part of the dex save. See the feat "Shield Master".
This is already in the PHB as part of the dex save. See the effects of cover.
Stand your ground and try to look tough so the dragon thinks you're impervious to fire.
I don't believe anything in the spell prohibits you from doing this. This sounds like a super rad idea though, I may have to steal it if I get a chance to be a player anytime soon.
Most are likely still Dex saves, but the results are different. The results are where the agency lays in something like this.
Other than that last one, the result all look the same to me. Avoid fire by dropping to the ground, result: damage avoided on success. Avoid fire by hiding behind shield, result: damage avoided on success. Avoid fire by hiding behind cover, result: damage avoided on success.
I don't think saves are there to limit you, they are there to give you fair, balanced default option, usually the one you would be most likely to pick in the first place. If your DM denies you from taking an option against a spell or effect that you logically should be able to take, that's more of a fault with your DM than the system.