Lol - Doh - /face plam
It never occurred to me that you could trigger the kiln with a hero (I assumed only a human player could do it) and that was what was making this seem hard.
Very simple
Standard perma-sin sliver armor build with Alkar's Alchemical Acid
If you don't have a human player you are running, flag a hero near the base of the pyramid where he won't trigger the kilns.
Run across the bridge and gather the destroyers together (the three ranged attackers by the east bridge will not cross the bridge and are no threat to the kilns so don't worry about them.)
Move almost to the choke point where you can can still clearly see the top of the pyramid and flag your hero to the top of the pyramid to trigger the kilns (to be honest this did not work every time. From that distance the hero seemed to get confused sometimes even though he only had to walk up the stairs. After little experimenting I was able to find a spot to the right and in front of the choke point that allowed me to set the hero pretty consistently)
Go to the choke point and wait out the heating process (use sliver armor to kill as many melee destroyers as you can while waiting for the kilns)
Once the kilns have heated, kill the bringers (Since you have killed most of the melee ones, targeting the bringers should not be a problem and the ranged attackers hitting you will bring them down quickly. You may lose agro on some of the destroyers when you go to kill the bringers. These will head to the kilns. That's not a problem if you kill the bringers quickly enough, and if you killed most of the melee fighters you should be able to do so. You can actually lose one kiln, but not both, at this point without failing the mission.)
If you are farming for cores instead of going for speed you can take all the time you want to kill destroyers before killing the bringers. But keep in mind if you lose agro on any of the destroyers, they will head for the kilns.
going for speed = just a few seconds over 7 minutes (not counting loading times) And after all the trial runs I am now 25 cores closer to the gloves
Course, it's not a true solo as you have a hero with you but it's close.