I repeated the strategy a few times and refined it to the point I'm very confident I can pull it off reliably. Fire Kaiser and Gaia Protect are effective gap-fillers, allowing me to nearly fully mitigate every Overdrive. The boss has one opportunity to use a Rage Overdrive in cycle 2; if it's the double/triple buff, then I have to wait it out. Otherwise these are 10min clears. Charm from the Bursts does occasionally land and this can interfere with overdrive timing; cycle 2 is a particularly vulnerable point.
The strategy works identically outside Burst hour and that means I can do these runs whenever. I also tried without a 100% eidolon; the DPS shortage (I kept my 40/20 character ATK/HP eidolon) meant that I ended up facetanking a Rage Overdrive each cycle, but I still managed to pull off a victory with no deaths until the end (ultimately caused by Charm). Conversely, the DPS shortage meant I could pull off a Full Burst during Stun, which was useful. The fight took much longer and ultimately this is not an efficient way to clear.