I feel both the powders you have on hand should work pretty well. I have loaded that bullet in my 6mm Remington Model 600 (my son's rifle now) which has an 18 1/2 inch barrel. I used IMR4350 and it worked very well. His game load is a 100 gr. Partition in that rifle which also is loaded using IMR4350.
I have no load data on .243 Win. I do have a lot of experience with Sierra 85gr. HPBT & it is a great bullet for both Coyotes & Antelope. In my 6mm Rem I have shot some small groups with it & in my 700 BDL it averages around 2.2 inch groups for 3 shot groups at 300yds. I would not be afraid to shoot to 500 yds on Antelope with it & Coyotes.