Was the Mosin Nagant ever considered for USA use?

You seem to have a real fixation on the P-14 rifle. The only real advantage it had over most of it's WW I contemporaries is a better back sight. That isn't enough to elevate to the "fantastic" catagory. Most everything else is quality control of the rifles or ammo.

The other issues with the Chauchat are 1. if it jams with the barrel in the rearward position (or close to it) the ejection and feed ports are blocked off making working on stuck cases or double feeds rather difficult. 2. you have several pounds of barrel bouncing back and forth with every shot over a distance of nearly 3 inches (if not over on some versions) making for a LOT of vibration. Which combines with a rather spindly bipod to make long distance shooting difficult.
To be fair the Chauchat was NOT a light machinegun. It was an automatic rifle which is a different and often misunderstood catagory.

And what works on commercial hunting weapons firing 2-5 rounds may not be the type of action you really want to use on a combat automatic weapon.

It would take a very French man to say the Chauchat is brilliant but the idea is to say the Chauchat wasn't that bad.
I agree that the Chauchat was a hybrid between LMG and heavy rifle but considering the tech and wisdom of the day the Chauchat was certainly novel.
The long recoil system was chosen by the French and why I don't know. I chose the Model 8 purely as another example of the operation. There are advantages and disadvantages to everything so I would assume the choice was based on either solid engineering or the French being French. Which means they do as they wish!
Clearing a jam does look a nightmare but I'm sure that could be said for many other guns of ww1.
The recoil in full auto would be better than a AK-47 due to length, weight, bipod and very low rate of fire and would expect weapon to be fired prone. The metal mass movement is said to be lessened and the slow fire means it doesn't run away from the user. Long range probably isn't what the Chauchat was designed for.
The Chauchat was designed with a loader which is why it has the open mag so that would be more LMG.
As a British internet rifle fan, the P14 ticks all my boxes. Only I should really leave my true fanboy status for the P13!

I think that we can sum up that the Chauchat was certainly not a good LMG but neither was it a bad one and there were better but the US version was much worse. Would it be my choice from period designs? No but it was far better than relying on rifle fire if you have enough of them. Were this a poll for best WW1 LMG I would go with the Madsen. Expensive but excellent.

The Mosin Nagant was cheap, sturdy and accurate enough for it's task but offers nothing that could not be found with other period rifles. Again, were this a best WW1 poll, I would stick with the SMLE. Accurate enough, sturdy enough and a 10 round magazine. The P13/14/17 were the right answer, but to the wrong question as it turned out.

Considering the sheer volume of P14 and M1917 made then I would say right question and right answer.
Had it all gone to plan the British Tommy would have fought in the trenches with a 7mm P13.

Nothing really to add to the thread. It seems all has been covered.
Just can never let a thread about the Mosin go by without including this classic piece of humor.
It's a few years old now, so the prices are a bit out of date, but when this was created, they were selling at those prices.
...read the chart from left to right....

For just about all the bolt action rifles of the era, the practical differences in design are minor. Execution being more important. Quality in actual manufacture. Throw in the quality of the ammo or variations and trying to claim a design was better than another in combat with, for most part, poorly trained troops doesn't really work very well. Way too many variables.
P-13 series had about the best rear sight in WW I but that only counts if the troops are really trained to use it and if they actually do use it in combat. It's heavier barrel may have resisted pressure from warped wood better.
The SMLE was easier to clean the dirt/mud out of when (not if) you got crud in the action.
And so on.
Uniform barrel dimensions and good chambers had more to do with accuracy than the actual design of the action. However oversized chambers were more tolerant of dirty ammo. Rimmed cartridges tolerate oversize chambers better.
If all had gone according to plan the surviving British Tommy's would have done more than hang the committee members who voted for the P-13 in effigy.
Numbers don't mean a whole lot. They made more Hungarian M1895 Mannlichers than they did P13/P14/1917s.

Of course, with the way history went then yes taking on the P-13 would have been a mistake and glad they didn't.
Had there been no ww1 then with the ammo issue resolved then the P-13 would have appeared sometime maybe 1916. Since it's basically a Mauser then it's no better or worse than a K98 or the M1917 the Americans used.
This is one of those what ifs where the alternative history is worse than what actually transpired. The SMLE was kept on and that was the better outcome.