I play pyro Tanya as my secondary, and I don't see what would stop Kotal from just backing himself into a corner and using Sun Ray to mitigate all the chip damage and force her to come in (with the way her zoning works, you'd be free to whiff air throws too). I'm speaking from a pyro Tanya versus Sun God KK right now, so I'd need help ironing out why the other variations would be able to handle this.
Yes, she would build tons of meter for EX dust... breaker, and EX teleports, but none that would actually make a dent in Sun Ray's healing. She is required to come to you eventually, and at half screen you're just waiting for dust so you can block it. You can keep jumping back so that way if she runs in you get JB 1, and if she stops to dust you can avoid trip guard and land blocking. She's at -4 on block, so f+1~air throw can get you in safely and force her to armor out with something. If you catch her with jump back 1 (air or ground), she's losing 40% health unless she spends meter to break.
From Sun God's standpoint, as long as we have one bar for EX SGC... she can't mix us up in close because we'll just eat the attack and throw her. Blood God would be riskier with the parry, but it would work the same since most of her specials only have one hit. Her overhead/low mix up string options give you time to block/backdash out of the rest, so I can't find the issue. She's one of the few characters I run away from and heal when I fight her.
I haven't played a tourney ready Tanya yet, but from the ones I've played... I don't see where there is a fundamental problem.