Rank vs. Position. How does an E5 Platoon Sergeant deal with an insubordinate E6 in his Platoon?

You take it to your Platoon Leader. Here is what I mean by this: By position you outrank him, therefore you can administer corrective training. Since you do not outrank him by stripes, your platoon leader is their rater. If you are having issues with this SSG not adhering to your platoon sergeantship duties and orders, you should have a sit down with this SSG, the PL, and yourself...this way, there will be no misunderstandings as to where each person sits on the food chain. Before all three of you sit down, you should have a sit down with the LT to ensure they have your back and will support you. Also, when you counsel the SSG (Which you can do since you outrank them by position), establish every single LEFT/RIGHT boundaries that they have and your expectations of said SSG.

You do not out rank him. By AR 600-20 the first determination of seniority is grade. With-in grade there are precedents concerning DOR and other factors that determine seniority. Under the Army Command Policy regulation you cannot be de facto senior to this SSG.
What does potentially apply in your situation; although, it should not apply unless the SSG has been formally relieved is para 2-b, AR600-20 which states in part: "However, commanders subdivide responsibility and authority and assign portions of both to various subordinate commanders and staff members. In this way, a proper degree of responsibility becomes inherent in each command echelon. Commanders delegate sufficient authority to Soldiers in the chain of command to accomplish their assigned duties, and commanders may hold these Soldiers responsible for their actions. Commanders who assign responsibility and authority to their subordinates still retain the overall responsibility for the actions of their commands.
This authority can only be granted by the Commander (not the platoon leader, first sergeant, etc) and it should be done by formally to include notifying the SSG you are acting on Commander's behalf. That is a lot of responsibility for a Commander to place on a SGT. If I was the Commander, I would either put the SSG in the Platoon Sergeant position and hold his feet to the fire or move him under a more senior NCO or Officer that can give him lawful/direct orders using their own authority bestowed by their rank. Additionally, that senior person and can also rate the SSG. Even with the Commander's authority you won't be able to rate the soldier.

I agree with SFC Livingston, get your chain of command involved and establish some boundaries, not sure if this soldier is a rag bag or just someone who leadership does not suit. I know when I was a squad leader for the WWTU, I had a SFC and a MSG assigned to my squad.