From my experience I think the lightest bullet I would use is 400 gr. Lighter bullets are OK for hunting but at 300 yds. I think 400 + gr. will serve you better.

Brownie

My thoughs is a round nose 350 grain or a flat nose or round nose 400 grain would be good.  Will have to do some testing and load developing in your rifle to see what works best.  A 300 might even work, but may be hard to keep velocities in the range you want and still make it the 300 yards.

dave

I have a freind that shoots a 350 Gr bullet in a Original Sharps Long Range. The bullet is the solid nose version of the Gould Hollow point. I reworked the base band so it cast .461 Diameter as the Sharps Groove is .462 Diameter. This shoots super at 200 Yds with 50 Grains of Fg Black with Corn meal Slightly compressed over it to keep it all together. Do not know what it would do at 300 Yds. HTH Regards, FITZ.

What is the target; paper, or steel knockdowns?   might make a difference in bullet Choice  as will the teist rate of the barrel.  I'm assuming you'll be shooting fixed ammo; breech seating and shooting prone could be a complex PITA.
If I were shooting prone I'd look to find shoulder friendly loads,  although you might try a back position if allowed.  
My limited experience shooting 45-70s off the bench with heavier bullets = BP is more of a hassle to load than smokeless, but it seemed to me to be more shooter friendly.   I'd probably go with a BP express load, twist permitting, and consider duplexing if the match rules permit.

Does anyone have a mold number for that Gould bullet?  I just got a Ruger #1  S-1  45-70 and that sounds like that might make a good hunting bullet

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I believe the number is 457122, 290 HP and 330 Flat point.

Frank