I think the flaws won't stop Exar Kun.
It will take Ulic several days if not a week to get to Coruscant (provided he is on Yavin 4) while it will take a little less for Mandalore to get there, and only a few hours of the Koros fleet to get there. So their going to arrive in dribs and drabs (more so if a gravity well generator is involved) making for it easier for Xizor to destroy them with a constant influx of Black Sun forces who will pour in from across the galaxy. Either that or they will be forced to group together first, giving Xizor ample time to prepare.
Was Ulic ever on Yavin 4? I would assume he is in the Empress Teta system with the Krath fleet and some parts of the Mandalorian fleet. So going for Coruscant won't take long.
Traya will foresee Kun's attack on Malachor, and will foresee her defeat. She will therefore escape Malachor with her fleet on the Ravager. Kun will then have to navigate the hazards of Malachor V (landing an army of Massasi warriors in ancient, dodgy vessels on a planet coated in electrical storms and with a strong gravity pull will be difficult) and fight his way through the academy only to find Traya is not there. He will likely search the place top to bottom giving the inhabitants plenty of opportunities to whittle away at this Brotherhood and set traps for the Massassi. Hey they could even sabotage the ships, leaving them trapped on Malachor. (But the ships would probably crash anyway :P) His warriors will probably all die on Malachor, but I'm sure Kun can use his various powers to conjure up some sort of serviceable vessel to get him off the planet.
Leaving Kun an academy behind will backfire. Kun will take the Sith teachings he can get there and use them. This will only make hin stronger.
Btw. Kun will sese when Traya has left.
[*]The majority of Kun's fleet - the Tetan Navy - is based in the Deep Core, several weeks away from Yavin 4 and Malachor V. He cannot rely on their assistance to invade Malachor V and will have to solely dedicate them to attacking Coruscant. The Mandalorian Fleet will be split between invading Malachor, protecting Mandalore and protecting Yavin 4. Traya will therefore be able to break through any Mandalorian blockade of Yavin 4 fairly easily. And set up an ambush. For example she could leave her fleet lying in wait, invade his Temple (all the Massassi warriors are trapped on Malachor V) and trash anything of value, and set up an ambush there with 4 other Sith Lords, including Sion the Immortal. When Kun returns from his failed mission his small fleet is ambushed by the full forces of Traya's armada AKA everything. If Kun manages to escape to the surface he'll find himself subject either to orbital bombardment (and unable to protect himself through rituals due to the desecration of his temple) or ambushed by Traya and her most powerful Sith.
Kun will know where Traya is and will go to find her. If she is on her ship, he will land there, if she is on the surface, he will go there. Then he will use his amulet to knock out the other Sith, Force-persuade Sion into dying within a very short time and then kill Traya.
(Btw. I agree that, Revan and Traya are better strategists than Kun on the long term. The Republic would have outlasted Kun/would have sprung back into existance after his Empire crumbled. But in the Kaggath, it doesn't matter because he can win on the short term.)