I really like the Idea of a 300 WSM. I know you looking for low recoil. Which if you put this is an ultralight rifle with no brake or can, it would be quite rough to shoot. But with a shorter barrel and running some lighter copper bullets in a decent weighted rifle with a can, I dont know if that would really bother anyone. Also for a moose, people are generally getting more than 2 shots into that animal, they just dont react like a deer. They will soak up lead like nothing else and just continue to stand there. So maybe a little lighter of a rifle in something like a 270 win or a 6.5 prc with tough bullets. focus on quick follow up shots and shot placement.
So I recently built a tikka roughtech ranch .308 with a 16” barrel. (not sure they are still making it) I have really liked this rifle. the stock is not bad for a tikka (not as flimsy as the superlight) and it shoots well. I wish it had a slower twist to make the 130’s a little more accruate but I am shooting 1 MOA pretty regular. I live in Louisiana and 90% of my shots will be within 400 yards and I wanted the maneuverability of the short rifle. I have a banish backcountry can on the front which keeps me pretty short. I have been shooting the barnes TTSX 130 grain bullet and am averaging 2920FPS at the muzzle. I am at 2000fps at 400 yards. This is factory ammo so I may be able to up the velocity a little if I reloaded but for my purposes it performs very well. I have shot it out to 500ish on the range. It is a fun rifle and it is my new go to for most of what I do. at 300 yards the energy is 1361 at 21xxfps. Other rounds I have shot are the Nosler accubond 165 (2600fps), 150 swift Sirocco (2640fps).
I also have a 35 whelen in a CVA scout that I cut the barrel to 20 inches. Now I shoot with a suppressor (omega 36m) and with a break action 20 inch barrel I would not like shooting it without the suppressor. I am shooting the 180 barnes TTSX and my last average velocity was surprisingly, 2970 which is close to if not over box. according to my ballistic calculator it drops below 2000 fps at 325 yards. now with a 22 or 24 inch barrel with a break on it (I can say even with a break it kicks hard, thus why I wanted it suppressed.) you could probably move that out further. or a bolt 35 whelen in a heavier rifle will reduce that recoil as well.
I do not own one but love the idea of the 338 federal. I have an old .308 that i am seriously contemplating re-barreling for the 338. Buffalo bore loads for it but you could probably get more out of it reloading.
Who tee who just did a video with a Savage rifle he found in 338 federal, fun video to watch… agree with him on why is this cartridge not as popular? Maybe Federal needs to do a Re-Realease party for it!
He sure can come up with some odd ones! 
one of these days he will probably show up with a Lazzeronni!
The 338 Federal was invented right about the same time that the 6.5 Creedmoor was. Everyone decided to go in the light recoiling, high ballistic coefficient Direction instead of the big heavy rounded 338.
Maybe if they gave it the backcountry treatment we could have a resurgence
I have never been moose hunting, but from what I have heard, they are not hard to kill. I would think a well placed 6.5cm or prc would do the trick.
I havnt hunted moose but I wouldn’t use my 6.5prc. Id use my 300 win mag Backstop buttpad and Banish Backcountry suppressor 180g tsx handloads, or my Ruger Guide Gun in 375 Ruger Area419 Sidewinder brake 270 G ttsx handloads.
Hope your hunt is successful.
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It’s kind of funny, if you follow John McAdams podcast he has done several episodes titled “ the best cartridge for everything” where he and his guest will go through everything from a tiny deer up to dangerous game in Africa and choose a cartridge and bullet for each.
Every time they come to Moose, everybody always says they’re not hard to kill, they don’t need a big bullet. But then, when they are asked what they would choose they all choose something like a 300PRC, RUM, 338 WinMag, etc,etc.
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It’s cause traditional where their is moose theirs brown bears and you would want a 30 cal or larger to kill brown bear
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