I found a bunch of unpublished M40 series docs at the National Archives and in the mid to late 1990's they start to talk about updating the aging M40A1 and you see the ground work start for the M40A3.
I see them state in the wind up to the new program that they were having a hard time getting the HS Precision barrels to shoot accurately. So they mention for the new updated M40 series rifle they would like to switch back to Hart, with alternatives of Schneider and Douglass. They detail all three were "Buttoned rifled barrels." They also detail that Schneider was very similar to Hart and was actually the barrel maker for the Army Shooting teams.
Next I see them do a barrel endurance test with the Schneider's in Dec 1997 on some newly built M40A1s and they were thoroughly impressed with how well the Schneider shot even exceeding nearly 3x their desired maximum round count for barrels. So they seem extremely impressed with Schneider barrels from that moment on.
The short of this is, they built the first test M40A3's around May 1999 and by then it seems Schneider was firmly established as the barrel maker. Then in 2001 when I see all the information on the barrels turned into Headquarters Marines for the orders to buy the parts to build the M40a3's, they detail the Schneider is the only barrel that meets the precision qualification of the M40A3. They once again reference the Dec 1997 endurance trials as proof that Schneider was the only choice. There are also mentions that they were the only manufacturer that could produce the barrel in the quantities they needed, in the timeframe required.
Talking to guys who were involved in the testing at PWS during this time, it sounds like there were a lot of things tested all the time. As companies were always submitting items to try to get a Govt Contract. A lot of that testing would have never made the official documents, so I'm sure a lot of stuff was tested that was never recorded and wouldn't be known by anyone unless you were there. So that is always a possibility. But at least from the official documents I found at the archives, Schneider seems to have been the choice even from the beginning.