Complexity class for polynomial algorithm for 3SAT, but with exponentially large values?
Complexity classes are classes of problems, not classes of algorithms. For example, the existence of Dijkstra's algorithm means that the problem of computing shortest paths in graphs is in&nbsp;P, but it doesn't make sense to say that "Dijkstra's algorithm is in&nbsp;P".

Exponentially large values can be stored in binary in a polynomial numebr of bits, and we can compute on such numbers using a polynomial number of operations. This notwithstanding, it seems that you're trying to get a polnomial-time algorithm that somehow dows exponentially much work, which is an oxymoron.