The 1907 was an interesting rifle with fairly colorful history for such an obscure weapon.
It saw service in WWI with the French military, allied aviators, and one US Military unit working in the US during the conflict (National Guard, IIRC).
It was quickly embraced as a lawman's rifle, and saw extensive use with the Texas Rangers as well as the FBI. Many criminals of the era also made use of the weapon.
Interestingly, it resurfaced again in the 1950s - seems Winchester decided to make another run utilizing NOS parts though the rifle had been out of production for decades. Those rifles were marketed and quickly picked up by law enforcement agencies.
Given it's autoloading mechanism, available 10-round magazines, and respectable ballistics of the .351 Winchester cartridge, it truly was revolutionary and I've always found it surprising that wasn't more military interest in that concept for several years.
Regarding the OP, I'm not aware of any great sources of ammo. The Old Western Scrounger does have contemporary loaded .351 Winchester rounds made from .357 Maximum brass.