@Chicken76
I think it's one of those things you'd have to try and see if it'll work out for you in the end. Your cases airflow sounds adequate to keep your internal temps within reason. Depending on the case I'd imagine it would somewhat dampen the sound of the stock cooler. Without trying it I'd say you'd never know in the end. If it was me I'd probably at least try it out before purchasing a alternative solution.
I'd imagine a constant sound profile from your PC during the dead of night would be best. Whichever way you decide to go it might be best to just use a fixed fan speed for your cpu cooler as they're nothing more annoying than a fan ramping up and down constantly with varying loads. I'm also thinking that depending on where your pc is placed or even aimed at in the other room could effect the sound in your bedroom.
I tried the 3600's stock cooler and wound up quickly upgrading it to a Arctic Freezer eSports DUO as it couldn't hang during prolonged all core loads. When I decided to upgrade to the 3700x I just went with the Arctic cooler from the getgo as I already had it so I have no idea of how the temps and sound profile would be on a 3700x.
I'm currently using the 3700x's stock cooler on another build that I'm slowly piecing together. Currently it's just sitting on top of the MB box and during similar loads to your intended use case scenario it keeps the 3600 in check, but does ramp up to around 3k rpm with my motherboards default fan profile. It's audible on top of the box, but not really to bad. I'd imagine it would be much quieter in a case.