I agree with you on everything but how you explained rotation.

Wait for DOTS to almost fall off before using contagion, fester like said and whenever you can when all 3 dots are up.
I would use ruin I, simply due to the fact its double MP for same damage, the insta cast is ok, but after one cast you wont be casting any faster than ruin I.
Also use Swiftcast on ifrit egi for Enkindle then bring garuda back out. Reason being is the ifrit skill has a DOT, hence more damage.

Your aim is to keep all of your DOTs up, and use contagion to extend the ones you cast with raging strikes.