I believe the person who asked required the opamp to be pin compatible with 4556 in DIP8 or soic8 in Objective 2, at least easily convertible.
Like I said, it's not stupid with measurements, rolling meaning swapping one by one. You don't know how one device would perform when such condition is not specified in data sheet. Like two opamps in parallel and loaded by a 32 or 16ohm headphone. And I agree without measurements, all the sonic improvements are basically bs.
Now onto whether you can improve a competent design. That depends on what competent means. O2 was designed for cost performance 4556 is basically the one of the cheapest opamp with 100ma current capability, using two opamps in each 4556 in parallel doubles the current to 200ma+ taking the advantage of the low cost. If it's opa827, that requires 4 pieces of opa827 which isn't cheap for even a single part tho you can achieve sub 0.0002% thd with 32ohm load and taking the advantage of fet input not dependent to source impedance and having ultra low offset. Also it's possible to use only one side of opa1622 for each channel and achieve better performance when not exceeding the output capability.