No mate, I gave up on the Chameleon to power the Factors because I thought they were drawing to much current, even at 12V. So I switched to to a Yankee PS-M2; a rather rare power supply made in Poland. Does the trick. It turns out, though, that my worries about the Chameleon may have been unfounded after all because I think the issue that aroused my suspicions – units turning on/off at random – was probably caused by worn out DC inputs on the Factors themselves.
Thanks for the heads up on the replacement parts. If I had the skill I'd do that replacement myself, but alas.. So I'll let Eventide's service agent in Australia do it (when the finally get the parts..)