3SAT solvable in polynomial time...but with exponential tuning?
If the tuning parameters depend on the entire input, then it's not a self-contained algorithm, so it says nothing about whether 3SAT is in P.

After all, I can give you an algorithm that has that property: in my algorithm, the 'tuning parameter' for a 3SAT formula $\varphi$ is 0 or 1, according to whether the formula $\varphi$ is satisfiable or not.  My algorithm ignores the formula on its input and just outputs its tuning parameter.  Sure, it may take exponential time to find the right tuning parameter for any particular formula, but once you've got it, my algorithm can output the right solution in polynomial time -- in fact, in just $O(1)$ time.  Yet this says nothing about whether 3SAT is in P or not.