Tips for efficient practice and teaching the kids to shoot further

[CMF]

We haven't shot past 300yds, but I'm wanting the kids to start getting more practice at longer rangers, both to increase their range and increase their accuracy at shorter distances. We typically are getting within 100-200yds if rifle hunting, but most of our wester hunts have been Muzzy, so even closer. and I mostly bow hunt.
My daughter drew a late rifle elk in AZ and I'd like to see her proficient to at least 400 if possible. I've seen her shoot smaller than baseball groups at 200yd with just a tripod.
We do a lot of outdoor activities so we don't shoot as often as we should. That said, how can we make the time we are shooting the most efficient and get the most rounds down range. I'm working in New Mexico currently so we actually have plenty BLM to practice on(very few places back in MS to shoot further than 2-300).
We typically shoot a few rounds walk down and check it out, cover up the holes etc, but the farther out you get the more time this takes.
I'm thinking of finding an area we can jump in the truck and run back and forth.
Maybe putting multiple targets and using more than one rifle before going back and forth.
I have an 8" steel target. and I have a mobile target stand I built. Should I get some bigger steel for further?
I'm guessing at some point the gun heating up will be a limitation?
What's your tips for getting the rounds in and teaching the young n's to shoot further?

 

[RWT]

IMO any new shooter it has to be fun with immediate feedback. I’ve use full cans/ 1 liters of beer or soda and shook them up between 100/200 yards.
I am also a big believer in clay pigeons. Easy to see, easy to hit, easy to spot with binos of you hit them. Once they can hit a clay consistently then make a game of tic tac toe out of it. Loser has to go down and clean up and winner determines where we eat dinner.