Searching for symbol except within subexpressions with a particular Head

Question

I would like to write a searcher like FreeQ that looks for a Symbol (or Head) in an expression, but confines its search outside of subexpressions that have a particular Head. Because expr can get huge, it is especially important to minimize the search time.

For example, I might want to test whether expr is free of Symbol=a outside of Head=func:

expr1 = a * b + c * func[a,x]

expr2 = b^2 + d * func[a,c]

Let's call this new searcher subFreeQ[expr_, symb_, head_]. Then I would like:

subFreeQ[expr1, a, func]
(*False*)

subFreeQ[expr2, a, func]
(*True*)

Answer 1

Just 'hiding' heads:

fq[ex_, a_, h_] := FreeQ[ex /. h[x__] :> Unique["x"], a],

e.g.

fq[b^2 + f[a] + g[a, x] + h[b, x, a], , (f | g | h)]

yields True