Advice from one that has been there and done that:
The 45-70 you have is plenty gun for mid range target. Properly loaded, it is just fine for long range target. You can start shooting both with that rifle now and search for a Remington Creedmoor while burning charcoal in your Sharps'.
I am pretty sure if you are looking at a "Remington Creedmoor" as opposed to a Sporting Rolling Block the 44 S will designate 44-77 if the rifle is unaltered. Additionally, some of the select 44 S Creedmoors were stamped LLHEPBURN on the bottom flat right in front of the receiver. Legend has it these were barrels tested and approved by LLHepburn for competition.
You will find the rifle of your dreams immediately after you spend all your money on one that does not quite measure up and at a bargain price no less.