I would choose something like a Nosler 150gr Accubond. Pushed at 2700fps it has sufficient energy to take elk size game cleanly at 500 and perhaps to 600 with good shot placement. The 7x57 is a fine old cartridge that will do anything the 7mm-08 will do plus a wee bit more. Piece below is about the 7mm-08 but as you can see the author sees little difference between the old Mauser and the newer Remington.
Personally I don't have any experience with 7x57 on elk. Seen more than a few taken with .270's and 30-06 though.
I load for my sister's 7x57, and RL-17 has given some great velocity in that case. Over 2900fps with a 140 accubond.
Like @wbm says, fine combo to 500, but 600 is pushing the envelope a bit.
If you're serious about stretching out there, it might be worthwhile considering the 162 ELD-M - they have a really high BC, and will carry a lot more energy out past 500. They also seem to have a lower threshold for expansion than a lot of other bullets. More retained energy and more expansion means more wounding at extended range.
I have a tough time recommending a soft target bullet as a general elk bullet though because, elk are tough! In my experience hunting elk, it's more likely to get a poor presentation at medium ranges than perfect presentation at distance. Sambar even more so!
I see you're from Aus. How many use a 7x57 for Sambar? Yes it will do the job, but it's not ideal. I saw in one of your videos you recovered a 180gr ttsx from a fallow deer, so Im sure you understand what I'm getting at.
Given the limitations of the cartridge, you might be best prepared by dual loading something like a 140gr monolithic (hammer/peregrine/cutting edge/barnes) for close encounters and an ELD-M for 500+?
In terms of being able to put animals down I'm not concerned, after all karamojo bell shot several hundred elephants with a 7x57 and i know a guy that has used them effectively on buffalo in Australia.
To be honest I dont plan on shooting to 600 yards, lost interest in anything that far. I think it's just better to over estimate my requirements than underestimate.
I've spoken with barnes, and planned on running 150 ttsx as they were the only thing in 7mm that will open up at as low a speed as they do (1500fps) but after four months on back order in aus with no signs of turning up i cancelled the order. I have ordered in some norma oryx for my in close stuff and I'll shoot that with open sights but with a bc of .33 they're not ideal for anything thats a poke. I'm putting a qr ring on and want a scope sighted to something more suited to longer range for sambar. Something like an eld or nosler long range has crossed my mind.
The Hornady 154 interlock or the SST is a pretty good game bullet for the 7x57 and they don't cost an arm and a leg. The SST would be the best for the longer range. I have loaded these down to 2500 fps with IMR 4350 to keep them safe to use in a friends small ring Mauser 7x57 but even at this slow velocity it has really done a great job for him on a number of deer to a little over 300 yards. If you load it up to modern rifle pressures to 2800 to 2900 fps out to 600 yards would be no trouble. I used these in 7mm Rem mag at over 3000 fps for deer and my buddy killed a pretty good elk with the 154 Interlock out of his 7mm Rem mag right at 400 yards. One shot to the bowler room and it stumbled about 3 steps and dropped dead. Bullet took off top of the heart got both lungs and exited.
I have always had good luck with Nosler Partitions.They shoot accurately in everything I have including 7mm/08, 30-06, 338-06. I would guess 140 or 150 grain would work well. They may be old school but they shoot accurately and penetrate well.
7mm08 is my primary rifle. 7x57 is slightly faster when loaded to modern pressures.
Its hard to beat a partition when you need a tough bullet. 140, 150, 160 grain
If you are hung up on BC, accubonds are slicker. 140 and 160 grain
I shoot more sierra game kings than anything. 140, 150, 160 grain
I've had good accuracy on paper with 150 ELDX, but haven't used it on game.
As mentioned above, 154SST is a great option.
Shot placements is what counts.
140: RL17, RL16, W760, Big Game, will get you 2,900+ fps (IMR4350 accurate as well, just a little slower, H4350 also a valid option but bulky in 7mm08)
150/154: RL17, RL16, W760, Hunter, will get you 2,800+ fps
160: RL17, W760, RL19 will get you an honest 2,700fps
On paper, RL26 is an option with 160s, but haven't tried it.
As was mentioned the 7/08 and the 7x57 are close. I would not use either at 600 yds for elk, but if forced to do so I would load the 145 Barnes LRX to appx 2900 ft/sec. This is the bullet I use in my 7/08 for deer sized game when the ranges get to be long.