I haven't reloaded in years
Currently trying the hornady superperformance 117 gr SST facory loads
If you aren't handloading for the 257 Roberts, you're really missing out on its potential.
Even the Plus P ammo offered is loaded down because so many rifles were built on everything from M91 to M98 Mausers and similar strength rifles.
I saw one several decades back, which was built on an 1888 Commission Rifle, that had its magazine altered by Turkey so it didn't require en blocs for feeding. Beautiful rifle, with exress style, flip up rear sight blades for different ranges which were right on POA when the cartridges were loaded to the proprietary recipe for this particular rifle. Very old school, but it had been designed and used for getting "meat" animals while on Safari in South Africa.
I had the same Winchester Mod 70 FTW as you show in your pics at one time, I ruined the barrel shooting powder that had gone bad and not cleaning it soon enough afterwards.
One thing you may find with your rifle is that it may not shoot boat tail bullets or bullets heavier than 100 grains well, because of the twist rate.
My rifle was one of the early production units in that model of Winchester and it had a "SLOW" 1-12 twist rate. Many other manufacturers used this twist rate and some even used 1-14.
My present Remington 700 Classic has a 1-10 twist rate and even with that, loading the 115-120 grain bullets can be tedious, depending on bullet design.
My go to load for this rifle is 46.0 grains of W760/H414, over CCI 250, under 100 grain Hornady #2540 Inter Loc = 3000fps for consistent sub moa out past 300yds.
Most of the Win Mod 70 FWT rifles I've come across have the 1-10 twist rate, but it wouldn't hurt to check your rifle.
Of the half dozen 257 Roberts chambered rifles I've owned, the best shooter was built on an M96 Mauser action, with a 1-14 twist rate, shooting 85 grain bullets at 3200fps with 47.0 grains of W760 over CCI250 primers, through a Douglas Match Grade barrel. It would barely stabilize a 100 grain flat base bullet, but everything 90 gains or less worked well. Seeing as it was dedicated to Coyotes, nothing heavier was needed. Half moa was doable with some bullet designs predictably on a consistent basis.