Except that makes it a universe all its own, unrelated to the rest of the DC cartoons - which make the reference to it in the Justice League/Static Shock crossover strange, at best.
You’re arguing at cross-purposes here, actually. First you mention (rightly) that the cartoon is out of continuity for the comics. Then you mention (correctly) that in the comics, it was Dick that had a romance with Starfire.
However, as you’ve already stated, the TT cartoon doesn’t follow the comics, so there’s no reason the Robin/Starfire romance couldn’t be used without reverting Robin to Dick.
Yes, the TT cartoon is incongruous to the comics - all the cartoons are.
Some Batman related examples (I know Superman had some, but I can’t think of them, ATM, and even beginning to list how Justice League diverges from comic canon would take way too long.):
Batman skipped the Jason Todd Robin, going straight from Dick to Tim.
Dick was never Robin when he was in his early teens. (He appears to be about 18 when he first appears.)
Barbara Gordon was still Batgirl last we saw her in the present, and, based on Beyond, is not going to be crippled in the future of the animated DCU.
Some major, non-debatable, diversions in TT:
The Teen Titans didn’t start as a group of sidekicks.
Speedy and Aqualad weren’t original members. (I don’t think Kid Flash even exists in the animated universe. If they do introduce him, no doubt it’ll be Bart, since the JL flash seems to be Wally.)
And a general one:
Static Shock and the Justice League both exist in the same universe.
OK, so…the various cartoons are out of comics canon. You’ll have to find some good indicators that the TT cartoon is out of the animated continuity for it to be Dick, since the current Robin in the animated universe (the one Batman mentioned had joined the Titans in the JL/SS x-over) is Tim.