Every time the solar summons mephits, it has to give them orders to glitterdust the area if anything suspicious happens. Possibly including special orders for a specific attack pattern. Same goes for telling the Avorals that they are to heal it when injured. Otherwise, they attack the enemy to the best of their ability, per the spell description.
Does the solar have telepathy? I missed the glaringly obvious summon monster at will, so even though I can't see it, I'm nervous. If not, the kobold has a general idea where the solar is after the first summon in the guard routine. It can also observe the full guard routine and know exactly when the monsters are going to poof out, *and* their exact strategy, since it's been dictated to them by the solar. Otherwise, their strategy is "attack the monster you can't see." So it knows the solar's orders for how the mephits are to glitterdust the area, and can stand where they aren't. If this means standing outside a 30' range of all of them, it can still off a mephit with its regular damage, and try not to giggle as the whole crew goes nuts.
Also, if the solar does manage to hit the kobold with waves of exhaustion or other spell, its invisibility will drop, and it is a standard action to restore. And while leaving and coming back with a forbiddance scroll is rather specific to the challenge, adding a +strength item is both a reasonable and affordable precaution for both this and other, unspecified encounters, especially since encumbrance is a known risk for low strength characters.
In short, even if we add the requirement that the kobold cannot leave and come back, he is nowhere near dead in the water yet.