If it's a properly built monolithic, built along the lines of a Barnes, then you can zing the heck out of it.
I don't have experience with the .45-70 Barnes or the Hornady bullet in question, but have used the TSX and TTSX in other calibers. I push them HARD, and they penetrate very, very good, especially if bone is encountered. They hold up well at close range and perform satisfactorily at longer range, though I believe Cup-n-Core bullets are better for reduced velocity.
The TSX and TTSX are the only bullets I have used that consistently penetrated Whitetails through and through from my .243 at close range, none of the 100 grain Cup-n-Cores are up to that impact level. I am going to try, on recommendation, the 95 grain NBT this year, but I won't be surprised if it fails to completely pass through a deer at 20 to 50 yards.
As has been pointed out, though, you will lose speed fast at the longer ranges. Though a 250 grain monolithic bullet will have the length of a heavier bullet, it still will be a little ways from the ideal SD of a .45 caliber bullet for use at distance. Once they start to lose speed, it's like they have the brakes on.
If it were me, I'd run them hard and stay at intermediate ranges. But I bet they'd work like gangbusters to 150 or so yards.