Welcome, Steve!
Full nitro .577 on a Ruger No.1 would generate absolutely stupid recoil! There was a .500 NE in Darwin for a while, owned by Norm C_, which ended up going with Ian D_ to NZ IIRC. Vinnicomb engraved and Waghorn stocked, nice to look at but an absolute bitch to fire. The .577 could only be worse!

The beauty of the single-shot is no barrel-regulation issues, so the sights can be set for any bullet weight and load you like. I'd recommend playing with the marvellous Woodleigh 650gr bullet, and work up a load with AR2208 or AR2209 till your teeth start to rattle, then back off a few grains!

If the weight can be increased to 10 lbs, 1650 fps with the 650gr Woodleigh is a great hunting combo. A rifle up towards 11 lbs should be manageable at up to 1800 fps MV.

..and if you're recoil-shy, I'd further recommend restocking with a forend and buttstock made of solid lead.