OP, IMHO you should just leave this old work horse of a rifle as is. It is unique unto itself because of its family history. As for being unsafe, there has been a lot of speculation and controversy regarding the sub 800,000 serial numbered 1903s. I don't believe there was ever a Kaboom on one that was used with issued ammo or even commercial ammo. The issues with those receivers came about because of improper case hardening. The people doing the job back in the early part of production did not have access to good optical pyrometers and mainly relied on each individual's eye to determine temperature by perceived levels of red. Of course not everyone sees things the same.
Some of the receivers were to hard and if dropped on a hard surface would crack. Later, when people got their hands on these rifles or just receivers they made changes to them that weakened them even more. If you've ever tried to unscrew a barrel off an early Springfield 1903 it can be a real chore. Supposedly some of these receivers cracked during the operation. I have had this happen with P14-17 Enfield receivers as well and I have never heard of them being declared unsafe.
Again, I would suggest leaving it as is unless there is something that obviously needs repair or the bore is badly pitted or rusted out or just worn out.
If it is fully operational, clean it up and for old times sake take the old girl out into the light and shoot her with factory ammo or handloads that don't exceed the pressures she was built to take.
Remember, all of these rifles were "blue pilled" with an over maximum pressure cartridge as a safety expedient before being issued. Treat that old girl with respect and she will perform as designed.
Also, back in the day that rifle was built there was a good chance it may have been purpose built as a sporting rifle and never put together in full military garb.
A complete refurb will cost you close to $750 by the time you source all of the parts in VG or better condition and have someone put it all together for you properly.
Someone like Purple that does very good restorations and is a member here could really help you more than I can. I just dabble in O3s and he goes in depth. I have seen his work and it is very good. Contact him by PM and he will likely ask for pics to give you an estimate from.
As mentioned, if it has been drilled and tapped or the bridge has been altered it can't be put into military configuration.