Upper bound for #Monotone k-SAT
A $k$-SAT instance over $n$ variables, monotone or otherwise, has at most $2^n - 2^{n-k}$ solutions.  This is simply the number of possible settings of the $n$ variables minus the least number of settings a single $k$-CNF clause can exclude, assuming all the variables in the clause are distinct.  You only have to consider the case of a formula with a single clause because adding more clauses can never increase the number of satisfying assignments.