The question you're begging there of course 'what IS classic Dragonlance, exactly?' And that's a question with no easy answer.
It's all relative of course. But, it makes me thing of the 1980's blunder for "New Coke." For those who recall, Coca-Cola decided it'd be a great idea (called an "intelligent risk") to adopt a new formula because of some taste tests. The greatest-of-all-time blunder was that those loyal to the brand didn't want it changed at all....because (drum roll for 66+ pages of comments)...it wasn't Coca-Cola anymore.
You can read back through dozens of posts about "what is Dragonlance," but there's a history lesson here. You try and rebrand something too much, too much from what makes it what it is (even if it's not as "tasty" as the original), and it's not Dragonlance anymore. It's a cheap substitute. As to the "core spirit?" It's high fantasy of "impossible odds" and saving the world, a stark contrast to prior D&D which had no 0 to level 15 adventure paths with one coherent story, which gave XP for killing monsters and getting loot anyway possible (even from fellow players). It was marketed in a way that hadn't been tried before and proved even "railroad" and "story-book" adventures could sell big and bring in new gamers who maybe didn't want to simply play "f*ck-around" campaigns by wandering around a hex-map till something cool happened.
Same with Dark Sun. Muls for instance - back in the original line, they were bred as gladiator slaves by sorcerer kings from human women and dwarf men (but never the other way around for some reason?) which inevitably resulted in the death of the human mother in childbirth.
I'll be nitpicky, and off-topic. Nowhere in the original AD&D boxed set nor the revised version was it ever suggested that Muls killed the human mother or required only human women. The only tagline was that they were a sterile product and often a product of breeding. Indeed, it wouldn't be sustainable if the mother always died. But the horrifying idea is there: this is a world without an afterlife, without religion, without universal mores that keep this type of thing from happening. Rich people actually breed poor people for amusement of the crowd. That's a bad guy right there. And, it's a roleplaying challenge. Muls don't have a culture, a universal history, a common language or identifying factor beyond their suffering. What defines you playing one? The same goes for half-giant. You're magically created. WTH do you even exist?
Same with Dragonlance. I don't think too many people are arguing in favour of keeping gully dwarves as a race of cowardly filth-wallowing comic parodies of developmentally disabled people, for instance. So how and how much do you change them - or any other setting element - while making the whole thing still 'feel' Dragonlancey?
Gully dwarves were praised constantly for their ability to survive in AD&D and 3rd edition. In the novels, they stood their ground in the Dwarfgate Wars and died to a man against insurmountable odds. Yet, their constant theme in DL and its novels is that because of what other dwarves (and humans) see them as, they are forgotten in history. Would America adopt a smelly, short, low-intelligence hero in its war of independence? Even if the winning general who led America through hard times was a gully dwarf, it wouldn't make for a good story for the masses. That's much more fitting for a Kharas. History is written by certain people to exemplify certain qualities. No history records any gully dwarf doing anything noteworthy. In the novels, this haunted certain characters, including Raistlin.
So don't change them. Leave them as is. They don't need to be a PC race, but if they are, let PCs see what they can do with their stats. Core D&D presumes you can't be successful with limitations in D&D as it doesn't allow scores to go below 8. Gully Dwarves should be just as capable (stat wise) as anyone else, right? Yet, D&D suggests by default a 5 INT character shouldn't be played, isn't worthy of being played, and won't be played with standard array. There's no reward in making a sub-standard character (stat wise) shine. Those with perceived disabilities don't get to shine. They get rewritten so their stats are the same as "normal" people.
Having personally played a character with a randomly rolled INT of 3 (and keeping him alive as a serious character who knew he was mentally limited and got upset when others would comment on this), I think the game loses something when we treat characters and potential races with "substandard" scores as something not worth playing.
[Warforged] Is it Dragonlance-y and in the spirit of classic Dragonlance? I reckon it is, though I'm sure others would disagree.
If you're saying gnomes created a sentient life on their own without intervention of the gods or Chaos, that would be incongruent with the pantheon of the setting. If you said "the Greygem of Gargath" infused spirits of golems with their crafters at the exact moment they were crafting, and this race thrived, that's more in line. I wouldn't disagree if it followed canon even if not an idea originally perpetuated by the writers.
Can you have a raging kender or gnome barbarian while staying true to the 'classic' Dragonlance spirit, and if not, are you reintroducing class/race limits? If the appearance and clothing etc style of the Plains people are redesigned to make them less of an obvious Native American rip-off, is that ok?
Class and race limits might be okay if you're trying to distinguish your setting from another. If you want "generic D&D" and "anything goes" and "everything fits," then sure, let tinker gnomes be barbarians and kender become wizards of high sorcery. It makes zero sense for the lore, history, and setting, but it works with the "generic D&D" mold. If you want Dragonlance, then there's a reason kender aren't wizards. There's a "roleplay" when you select a role, including one with preset limitations on what it can do.
It's a problem WOTC has been wrestling with since it bought TSR. Unique gaming worlds are awesome, big sellers, but they divide the market. If I'm playing Dark Sun, I'm not buying product for gnomes or wizardly organizations. I don't have a solution other than to remind WOTC that not everyone who buys Clue plays Monopoly, and there's a big enough market for more than one winner product.