Even with all your caveats, I don't think there is a good single answer to any of your questions w/o adding a lot other caveats such as - well which one works best empirically?   

Q1 - A 405 and 420 might work for you but I find anything shorter than a 450gr bullet to be pretty hard to work accurately in an 18 twist rifle.  But I shoot a bit faster than your .45-70 more than likely.  A slow rifle might make it work.  Otherwise I would say the 480 or 510 might be okay.  Impossible to tell w/o actually shooting them.  But I'd put my money on the 535 Postell.  The 570 may be too long to stabilize in your 18 twist.  Especially at ranges longer than a few hundred yds.  Again, ymmd

Q2 - I'd recommed the 535 for all of them.  But I don't think your .45-70 will be able to really stabilize any of them with accuracy out to 1500 or beyond.  Tthat's out of your rifle's class.  And you may have trouble even being allowed on the line in a long range match 800-1000 yds depending on the rules and your exact loads.

Q3 - Does the bullet really know what powder launched it?  Once it clears the muzzle it is on its own.  No, BP will not put a bullet out further than SP.  Physics are not specific to gunpowder.

Q4 - If you can't get 1300 fps (which you almost certainly will not) with the 535 postell, forget about 1500 yds.  What muzzle velocities are best are those that you find to be most accurate.  Shoot and find out.  The pressures are whatever they are.   

In short, take the 535 load it with a full case of whatever your favorite powder is and have at it.  My guess is that you will be in the sub 1200fps range, and will get very good accuracy out to 800 yds or so.  After that, you are going to have to do some fooling around to get the .45-70 to be sufficiently accurate and meet match requirements.   

Brent

PS.  When it comes to distances beyond 600 yds, I'm empirically deprived.

Brent,

          I have shot all of the following with my Sharps, the 405, 420, 480, 510, and the 535 Postell. My bullet moulds are the Lyman 405 making 420s with it, and I have the Lyman 535 Postell. All of the bullets that I mentioned shoot ok with my rifle. The 420 and the 535s shoot the best thus, which is why I chose to buy the bullet moulds for them. I have found stable loads for all of the mentioned bullets, better with the 420 and the 535s. I’ve heard what the 420s are ideal for the 200 yard shots. The 570 is not that much longer then my 535…I think that it will work well…just will not know how well until I get the mould and shoot that bullet. I wish that I knew someone that had some of those bullets for me to try before I buy the mould. I’m currently using 20:1 Lead. I do have some 30:1 and 25:1; lead to try out later. I’ve heard that the 20:1 was a good one to start with. Both my 420s and my 535s have a MV in the mid 1300s fps. I have a load for my 535 that I increased by ½ grain of powder that I’ll be shooting at the range this Wednesday. Just wanted to see what affect the ½-grain increase would do for me, and to see if I start to lead with it…it should put me in the low to mid 1400 fps. I would bet that you are right on the money with the 535s being my all purpose bullet. I have a long range shoot that I’m going too weather permitting in late October in Nevada. Shooting from 200 yards out to 800 yards and perhaps 1,000 yards. I shoot with a group of guys once a month at 200 yards and one of them has been shoot his Sharps at the Quigley without any problems. 

     Thanks for the simplicity of your answer to my third question. 

     As for your reply to my fourth question, I am able to reach the mid 1300s fps. I was trying to find out what bullet weights are most common that work at the long distances, and the various shorter ranges. You had some very good info that I do appreciate you taking the time to answer. 

MartiniBelgian,

     My question about the 1,500 yards did not mean that I had intended to shoot that distance, just wondered if it were with in my means with my rifle, I know that the 1.000 yards is, with the right bullet and load. I’m sure that both you and Brent are correct for me to stick with the 535 and that it being heavy would be more productive.