I designed a 2Ed "Wolf in the Fold" game once that used similar elements.
In it, the "Wolf" was an Assassin who was out to kill the Princess the party was guarding on her way to a marriage of convenience, sent by those forces who didn't want the war to end.
When I ran it for my usual group, players took me aside to say it was one of the most satisfying gaming experiences they'd ever had. (Lightning struck- I've only reached that pinnacle one other time.)
I was going to run it at a convention, but, for whatever reason, NONE of the RPGs drew any signups. Ah, well- I got my free admit.
As a con scenario, I had decided to hand each player a card. On one card, there would be a note saying "You are the Assassin" with a list of the Assassin's special abilities, limitations and resources.
My advice, based on my experience is this:
1) If you run it as part of a campaign, the Thing needs to be an NPC.
2) If you run it with a PC as the Thing, it will really only work as a one-shot, unless those who get killed (the Thing included) get to create new PCs afterwards.
3) Run your Thing like my Assassin. Yes, he has powerful special abilities, but he can only use them under certain circumstances.
Base him on the Changeling or Shifter race, and he's only able to use his more powerful true shapechanging abilities after absorbing enough blood & flesh- think of it like video game powerups- and he starts with zero. Perhaps you could use some of the Psionic powers to model the Thing's abilities, with the Thing gaining/recharging its PPs in kind of a vitality point system (like the UA alt magic system).