Stick with a 30 caliber. 300WSM is great. You'll get a bit more performance with a .300Win Mag. For the most from a .308 caliber you could go .300 PRC; .30 Nosler or .300 Rem Ultra Mag. But those are really not necessary unless you want an 800-1000yd gun. I have all those so aware of each pros/cons.
For bullets stick with Barnes 168 or 180gr TSX or TTSX as number 1 choice. Also 175 LRX, Other greats are Swift Sciroccos; Nosler Partitions and Hammer Hunters.
There is nothing wrong with the .30 caliber but I don't get the obsession with it for elk (because of diameter I guess). Per my earlier post the 6.5 loadeed with 156s is going to be comparable very quickly in Energy with both the .300 Mag and and WSM and beat them handily downrange catching up at 300 with the WSM and about 400 with the Win Mag. For the OP to get a better elk gun than what he's got he would have to get the 300 Weatherby, 30-378, RUM, exc. Maybe the .300 PRC.
In every comparison the .270 beats the 30-06, the 7mm-08 beats the .308 exc. The 6.5 PRC (and 7mm Rem Mag) is at least an overall equal to the .300 Win Mag. Yes you can load up the Win Mag with some heavier 210+bullets and max them out to keep up or beat the 6.5 PRC long range in energy and wind drift but you don't shoot as flat at hunting ranges and will want a brake on it at that point so why not get the real thing.
Likewise, something like the .27 Nosler is going to play very well with 160+ bullets and a fast twist with your big .300s with less recoil and a bit flatter.
Think back about every elk you have shot. I have shot all of mine with a .270 and one with a .300 Weatherby but it doesn't matter. You hit the lungs with that 130 .270 and it doesn't come out but it pulverizes the internals and they might drop or if some adrenaline already going run 100 yards. No different with your .300 Weatherby that puts a nice clean hole with a pretty big exit because the animal dies similar. With the .270 you have more internal bleeding and with the bigger bullet you get more bleeding and 2 holes. Has anyone ever lost an elk with a lung or heart shot with a rifle that you know or even had a hard tracking job?
Now there are a couple of shots where bullet construction and FE matter some but honestly how many elk do you know of that have been lost because you hit it in the shoulder or hip with a .270. I can see the argument for quarter shots and penetration perhaps but in real world situations you don't lose elk that way or at least its very rare.
You lose or have to track elk forever on gut shots, pass through shots that don't hit vitals, and extremity shots that may cripple a limb, but don't stop the elk from hobbling to the next county. The gut shots may be worse with a heavier bullet that passes through because that smaller fragmenting bullet tends to go all directions and might get to the liver and cause more internal bleeding or it might not. I think the pass through shots are more common with a bigger heavier bullet.
The craziest case I saw with an elk was a good bull that was hit at about 250 yards with a .300 RUM. It knocked him down like a rock and about a minute later when everyone was off guard he jumped up and ran straight uphill clearing the country. There was about a quart of blood where he fell but he was cooking with almost no blood trail in the snow. It is almost certain he was hit in that area between the lung cavity and the spine and the bullet probably missed the ribs at least on the way in. Now I don't know if things would have been different with my old .270 130 soft point but I do know that bullet would have exploded in there just from experience.
The only experience I have with a bad shot on an elk I have made was a very bad shot I made at about 400 yards on a cow. I hit her in the hip and it broke the bone. I had to track her about a mile and a half all downhill before she laid down and let me get within about 200 yards. The rest of the elk I have shot have dropped just as dead as a deer with the .270. The Weatherby worked great too and it was a quarter shot and a big bull so I'm glad I had it that day.
My dad killed most of the elk in his life with a 25-06 100grain, later a 7mm Rem with 139 grain. He has lately gone with a .300 RUM Bergara with a 26 inch barrel for practicality reasons on his elk hunts. He has a ranch that the elk come down to feed on at night and get up over the top of the mountain to the neighboring property pretty early. He has depredation tags and really gets tired of them eating his alfalfa all year, but he has to shoot them on his property which means long 500+ shots and he doesn't want to chase them to get off his property wounded and the really big .300 mags are the best for that, I will admit. He also doesn't haul that gun around but for a few hundred yards from his Kawasaki Mule. The reason those big bullets are better though is that he uses really high BC stuff like Bergers and ELDXs and pushes them out at 3100--3300 fps. Its the comparable velocities with a bigger bullets and comparable BCs that makes these rounds more devastating and you don't get that in your standard 30s because of velocity loss.
I am not knocking any of the advice or choices. But in actual elk hunting think hard about the scenarios. I am not at all like some of the guys on here that have hundreds of 1 shot kills with whatever rifle they like. I admire those guys but like most of us I am human and have a few misses and a couple bad shot placements. I have hunted enough to have seen quite a bit though and I am very sceptical of the mythical elk that only ran off because they were shot with .264, or .257, or .277 bullet instead of the mighty .30. The elk that take off and run uphill without a blood trail are either gutshot, not hit vitally, or don't have broken shoulders or hips. An elk hit good will go downhill and you will eventually get them. The gut shot ones will go all over the place and take some patience and on rare occasions get lost. I am unconvinced that in most of these circumstances that caliber would have made a difference and I don't believe that at except for the hot .30 or .338 mags. Bullet costruction yes, and that can be debated all day and is counterintuitive at best in some cases.
You lose wounded elk because of bad shooting, difficult shots, knocked off scopes, misranging, and all of the environmental factors that lead to bad shot placement. Confidence, comfort, and familiarity with gun and shooting techniques are probably #1 on this list. Use what you are most comfortable with and practice in real world conditions whether thats a 25-06 or a .338 Lapua with a 30 inch. If you like the Lapua and shoot it just as well it will be the better round with tradeoffs for weight and blast. Maybe it will even save you an elk but it won't if your thinking about recoil or get lazy hunting because of the extra weight and length or get it caught in the scabbard when getting off your horse.
I would like the more experienced elk hunters, guides, outfitters that have more experience seeing wounded elk to weigh in on this and offer a counterview. I just think a lot of this bigger diameter is better or that slower velocities with bigger bullets beats high velocities with medium weight and high BCs just doesn't pan out with the facts.