IDebugSymbols::GetNameByOffset and overloaded functions

Question

I'm using IDebugSymbols::GetNameByOffset and I'm finding that I get the same symbol name for different functions that overload the same name.

E.g. The code I'm looking up the symbols for might be as follows:

void SomeFunction(int) {..}
void SomeFunction(float) {..}

At runtime, when I have an address of an instruction from each of these functions I'd like to use GetNameByOffset and tell the two apart somehow. I've experimented with calling SetSymbolOptions toggling the SYMOPT_UNDNAME and SYMOPT_NO_CPP flags as documented here, but this didn't work.

Does anyone know how to tell these to symbols apart in the debugger engine universe?

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Edit: Please see me comment on the accepted answer for a minor amendment to the proposed solution.