Dragon Disciple is one of the classes ported over from 3.5 DnD. I don't remember exactly what the class was like there, but when Pathfinder first came out everything was supposed to be backwards compatible, so it likely couldn't add that much variety without losing that compatibility.
With that said, most (if not all?) spontaneous arcane casters are Charisma based, and the DD gives you bonuses to Strength, Constitution, and eventually Intelligence. With those stats (and a variety of magics) the DD should be able to cover any of the bases you described (you don't get bonus Dexterity, but you get enough Strength that you can put your highest stats in Dexterity and let the class bonuses carry your other physical stats).
Another thing you should check out if you're an old veteran who's new to Pathfinder is the BLOODRAGER base class. It's a Sorcerer/Barbarian hybrid, who can play a lot like a Dragon Disciple.
The only thing that changes the Dragon Discipline is that Kobold racial feat that lets you go through Dragon Discipline as a divine caster.
Kobolds also have a bunch of racial features and feats that go into detail about the color of their scales... breath weapon type, they have a mixed scales feat, all kinds of stuff pertaining to the colors of their scales, but I don't think any of them change the stat array. Some of these may provide you with some inspiration.
The stat array and classes/choices taken to get into Dragon Discipline is what determines what kind of dragon you want to be. The bonus stat increases are just a nice addition, and I don't think that you should be too willing to change them. Those additional increases shouldn't be a required part of the build, and you should have put your stats where they needed to be before entering the prestige class.
I am a quite recent re-entrant to the P&P hobby, after a hiatus of about twenty years. I kinda stumbled along into Pathfinder, which I like a lot.
Now, one of the more intriguing (potentially) prestige classes is the Dragon Disciple.
Something to consider here is that prestige classes are mostly dead in Pathfinder - better class design (with more and better class features beyond just spells), new hybrid-ish classes, and archetypes have pretty much taken their place.
In Pathfinder, if you want to play an arcane gish, you don't usually go Eldritch Knight or Dragon Disciple, but rather Bloodrager, Bard (possibly Archaeologist), Skald, Magus, Synthesist Summoner, or Questioner Investigator.
you should have put your stats where they needed to be before entering the prestige class.And that is where we differ in opinion. Tailoring the character from the outset to a specific goal/prestige class is at least partially min/maxing, IMNSHO.
I also disagree with VoodistMonk, you don't need to plan everything at the outset, and being surprised can be fun.
Having said that, if we're talking about min-maxing I feel like I should point out that you're talking about home-brewing a prestige class so that it gives you the stats you want ... that seems more min-maxed to me than just planning what you want your character to look like (I'd also like to say that I don't have a problem with min-maxing).
Back to the question at hand, I think that feats, spells, skills and even (or especially?) your choice of base-class can add a lot of flavour to your Dragon Disciple. Just as every cleric is different but gets the same spell-selection, every dragon can be different with the same stat bonuses. Really role-play is going to be the biggest differing factor.
It sounds like you've found a solution, and that does sound like a fun and interesting character, so I wish you all the best. Let us know how it goes.