Sledge,
Welcome to this board. We try to give as much information here as possible, and I try to keep up with things and still make bullets! So I'm sorry if I'm a little late getting an answer posted for you.
The .416 Remington is a natural when it comes to cast bullets. You really have to do something wrong not to make them shoot well. There are some things to keep in mind however.
You will need to use a Lyman "M" type of neck expanding die for best results and to keep the case mouth from shavin lead from the bullet, a real no-no when loading cast pills.
Also, when selecting powders you will also be best advised to use a powder with a burning rate much slower than you would for your full throttle loads. The idea here is to get a peak pressure as low as possible, and to have that pressure peak drawn out over as long a time as possible in the pressure curve, as a longer, more prolonged peak pressure is much easier on cast bullets than is a sharp, quick, short duration spike of pressure.
Lastly make sure that the bullets are seated to firmly engrave the rifling in your rifle when the loaded round is chambered. Cast bullets don't tolerate a jump into the rifling very well in fixed chamber guns. If you cant seat them to engage the rifling, at least seat them out to the longest practical C.O. L. that your magazine in the Model 70 will allow.
All that being out of the way now, I'll give you some loads that should work as a starting point with your desired 2000 fps target velocity in mind.
BTB 417"-375g LFNGC/78.0g IMR 4350/WLRP/Rem Brass/2050 fps
BTB 417"-375g LFNGC/80g H4831/Fed 215/Rem Brass/2030 fps
BTB 417"-375g LFNGC/83.0g H870/Fed 215/Rem Brass/2010 fps.
BTB 417"-375g LFNGC/84.0g WC870/Fed 215/Rem Brass/1980 fps.
BTB 417"-375g LFNGC/87.0g WC872/Fed 215/Rem Brass/1925 fps.
These loads are from a Lilja 26" barreled Sako action. Don't know if they will work for you, but should put you in the ballpark.
God Bless,
Marshall