Complexity lower bound: the gap between decision trees and RAMs
The natural model related to decision trees that can simulates RAMs is the branching program.  Basically, it is a decision tree with common subtrees coalesced yielding a DAG.   Time T and space S on a RAM can be simulated in height T and size 2^S on a branching program.  (You might need to use multi-way branching.)

For decision problems, it is clear that any decision tree only needs height = # inputs and space=total # of bits in the input.  Note that with multi-way branching one might have the # bits in the input larger than the usual measure of the # of inputs (e.g. n pointers each taking log n bits.)    For such problems with nlog n total input bits one can prove that certain problems cannot be solved in time O(n) and space=O(n) bits.  Is that the form of you problem?

You seem to suggest that you are using the # of outputs to try to get a larger lower bound.  It is usual for multi-output problems to allow many outputs along a single edge rather than at leaf nodes (see, for example, Borodin-Cook's 1982 paper on sorting lower bounds).  However, even without this assumption, one also can compute any function with height = # inputs and space = # input bits.  (Read and remember the input, and output all the values at each leaf node.)