Well, as a God style player, I'd pick Contagion, mainly because I believe you've mis-read the text.
From the PHB (Bolding the relevant bits)
Your touch inflicts disease. Make a melee spell attack against a creature within your reach. On a hit, you afflict the creature with a disease of your choice from any of the ones described below.
At the end of each of the target’s turns, it must make a Constitution saving throw. After failing three of these saving throws, the disease’s effects last for the duration, and the creature stops making these saves.
After succeeding on three of these saving throws, the creature recovers from the disease, and the spell ends.
The way I read it, the Creature suffers from the disease the moment you connect your melee spell attack. Causing a minimum of 3 rounds of which it makes it saving throws, whilst suffering from the attacks.
Pick the Slimy Doom, to disadvantage it's Constitution Saving Throws.... which it happens to be forced to make every turn
Meanwhile, have your attackers hit the creature and cause the stun effect to proc non stop.
Unfortunately, Sage Advice disagrees with you on this:
http://www.sageadvice.eu/2015/06/13/contagion-effects/
In our games, we generally will follow everything SA says (at least Crawford, Mearls can go off the reservation sometimes).
From a balance point of view, the spell seems pretty uber with your interpretation, so I can see why SA says what they do. With that ruling, it makes the spell much more a plot piece, rather than a real combat threat.
