I'd be curious to know what your load was for the 180 grain Noslers. I have a Rem 700 in 338 WM and with the plastic stock, it's a relatively lightweight rifle too. I think the key to keeping the recoil from being excessive is to keep the velocity at the lower end and if possible use a faster burning powder. I've been loading Nosler 210 grain Partitions and I've tried Ramshot Big Game, RL15, and RL16. I settled on RL16 for this hunting season but I'll be experimenting again with different powders and bullets now that I'm done hunting for the year. I've already got some Barnes 185's to try.
I think with your 180's RL15 would be good to try, and possibly Varget, IMR4064, and IMR4895 or H4895. These faster powders max out around 10 to 12 grains less than some of other more typical 338 WM powders such as RL19 and 4350, which helps to lessen recoil as your powder charge weighs less. You won't get quite as much velocity but still over 3,000 fps which is plenty.
The Nosler 180 Grain Noslers are sitting on top of 74 Grains of IMR 4350. I have not been to the range yet to find out what it is actually going to do yet. I used to have a Ruger M77 Mark II Stainless that sat in a laminated stock, it was heavy, and recoil wasn't really that bad, a buddy's 300 Win Mag in model 70 ( the synthetic blind magazine version that walmart was selling 15 years ago or so) kicked a lot harder, that was a violent recoiling gun. He fried the Simmons that came on it, then a bushnell that he bought , then a tasco, before settling on a Leupold. The Ruger I had had a burris fullfield II on it, and it survived for years.
I have a leupold on the Mossberg right now, and when I get to the range I will report back on what it does. I could not resist, I got it cheap, cheaper than what you can buy it anywhere in a store, pawn shop or online.
As far as what I will hunt with it. Whitetails, Wild Pigs, Bears. A Elk hunt hopefully one of these days. I shot a whitetail with my old ruger years ago with a 200 Grain Winchester Silver Tip at 180 yards, poked a hole on the way in, about a tennis ball sized hole on the way out, and the damage inside was like a grenade went off. The Deer dropped in its tracks.