Just buy a large AIO water cooler. Replace the included fans with Noctua. That is the full story of how I made my computer silent despite having a CPU with a TDP of over 200W.
Oh, c'mon, you weren't this specific. And I was. A 240mm rad is large by normal standards. Sure, a 360mm one is larger, but also usually not needed and you are likely to run into clearance issues.
I mounted it outside the case. Lots of cases have little cutouts to facilitate this. The fact you are sucking hot air into the radiator is probably not helping you.
360mm isn't needed, unless you want it to be quiet...
I have 8 Noctua fans in my PC and I can tell you they are not silent at 100%. Are they annoying at full power? Not really. But they aren't silent. Thus, fan curves are applied so that when air movement is not required, they aren't running at full speed.