Quietest? I believe right now, that’s the CGS Hyperion. Go to pewscience.com and look at his suppressor reviews. He has a breakdown of most of the current relevant silencers with ratings for everything. It’s more data than you’ll know what to do with I promise.
I don’t know what you know about silencers, but centerfire rifles are still loud. Definitely tolerable for a handful of shots, but still loud. I’ve never shot a 300 win mag suppressed, but I imagine it’ll be slightly less tolerable than others.
From what you need I would suggest the dead air nomad long titanium or the Hyperion.
you need to consider weight when hanging a can from a long hunting barrel. My first can a long time ago I had similar needs as you but I mad a mistake and got a really heavy can. Now I’m about to buy the standard length Nomad Ti. Under 10 oz if you direct thread it.
you should also consider getting a can with a universal rear mount so you have more flexibility with mounts. 1.375x24 is the way to go.