So, can somebody please help me understand why leveraging the same overload inside of those other methods is failing with that error?
Precisely because you’re using a dynamic value (param) as one of the arguments. That means it will use dynamic dispatch… but dynamic dispatch isn’t supported for extension methods.
The solution is simple though: just call the static method directly:
return SqlMapper.Query(_connection, sql, param, transaction,
buffered, commandTimeout, commandType);
(That’s assuming you really need param to be of type dynamic, of course… as noted in comments, you may well be fine to just change it to object.)