I would like to use this rifle for hunting and I'm looking for feedback as to the strength of the action and things to watch for.
I recommend that you replace your 60 + yr old mainspring with a new Wolff. I recommend using the 20 pounder mainspring and nothing heavier.
When you replace the mainspring, you will notice just how weak it has gotten over time.
What a new mainspring will do is quicken the firing pin strike, crispen the two stage trigger pull, and it may improve accuracy. I shot a ten shot group in a 03A3 with the original WWII mainspring, replaced it, and the next group was significantly better. I believe a snappy mainspring makes a difference. It will certainly reduce the chance of a misfire in cold weather.
The trade off will be a slightly heavier bolt lift and the trigger pull weight will increase. Neither of which were a bother in my rifles. I did swap cocking rods around to get the lightest bolt lift possible.
You did not include a picture, so I don't know the sights you have, the safety, etc.
Even though this is a double heat treat receiver, that does not mean it is made of "uber" materials. Rather it is made of steel that today, is considered adequate for low strength fasteners. Check Matweb on this.
http://www.matweb.com/search/DataSheet.aspx?MatGUID=4c43fd8ed4454e2d9301c408e80eab18 So don't try to magnitize this action. Shoot standard loads, use good brass, and all will be well.
http://www.gunsprings.com/RifleShotgun/Springfield_RsNF.html
SPRINGFIELD 1903 - All Modifications
BLITZSCHNELL Load-rated striker springs
Factory - Reference Only.: 16 Lb.
Ratings available.................: 20, 24, 26 and 30 Lb.
Stock No. 648xx.....$ 8.29 ea