At one time, I owned an as-issued 1903 Springfield with the serial number 800321, obviously one of the very first "high-number" '03s. The barrel date (original barrel) was February 1918, meaning that the manufacturing change occurred DURING WW I, not after the war. Note that in recent years, it was discovered that a limited number of rifles with numbers ABOVE 800,000 were in fact made with the older single-heat method. Not many rifles were involved, perhaps only a few dozen, but these were apparently rifles that were already in process when heat-treatment changed. All such rifles were numbered very close to the magic 800,000 figure.
Elmer Keith himself, writing about his time at Utah's Ogden Arsenal during WW II, told of simply fitting new bolts to low-number Springfields, checking the headspace, and firing a couple of standard PROOF LOADS (special high-pressure ammo for testing the safety of guns). He stated that no low-number rifles failed the proof test during his service at the Arsenal. These rifles were then released for normal issue and service.
Testing for "sufficient" reciever hardness is pointless. The faulty receivers are TOO HARD, to the point of brittleness. Dave LeGate, I think it was, writing in Rifle Magazine many years ago, described his disbelief in this brittleness...until he took an early 1903 receiver and tapped it lightly against a bench vise. The receiver shattered like glass, and he published photos to show the breakage.
I own and shoot a Rock Island low-number '03, professionally sporterized by my gunsmith Grandfather for one of his sons around 1950. The rifle was heavily used for over fifty years with factory ammo, until my Uncle's death a couple years ago, at which time it passed to me. It has seen extensive use here with cast bullets, and later this week it is travelling with me to Alberta for a deer/elk combo hunt. It won't be my "main" rifle, but rather goes along as a spare and/or iron-sight fallback. I consider it to be serviceable in all respects....but it IS still a low-number rifle, and I keep that in the back of my mind. It's a calculated risk, I suppose, but a low risk, given the rifle's performance history.