I'm shooting the Hornedy 139 SST's in my 280 Remington, but just for deer. Take the 8mm Rem mag elk hunting with Sierra 220 grain Game Kings. I'm sure the 7mm's work well as there's lots of elk killed here in Idaho with them, but I've always liked something bigger, but that's just me.
Every gun is different as to the bullets it likes and you've just got to do some experimenting to see which yours likes better. Every rifle I have seems to have a preference and finding that preference is the fun part of loading and shooting. I've often seen two identical rifles that would not shoot the same bullet well.
Keep on plunking those bullets downrange and you'll find one that works. As far as what takes an elk down, well that's a different proposition. I've seen elk wounded with about everything you can plunk at them, but of the 45 or so I've killed I've always used either a 300 mag with 180 grain bullets or since 1978 the 8mm mag with 220 grain bullets. Would I shoot one with the 280, well yes if that was all I had, but I'd do just like you or most sportsman do and be very careful with my shot.
I've a friend whose wife used to shoot her elk every fall with her 243 and hundred grain bullets. She always shot a cow and always kept her shots under a hundred yards and always took a neck shot or simply didn't shoot. She always harvested her elk. So smaller calibers will kill and like many say elk aren't bullet proof. Now that we've got a wolf infestation going she's retired her 243.
One of the reasons I like bigger bullets with more energy is I've packed some elk out of some really nasty places they've gone after being shot dead with my friends favorite 270 and they simply decided dead or not I'm going to run to the bottom of this canyon before I fall over. Three days later of packing, dragging, sweating, cursing, winching and trying to salvage the meat the weather is trying to spoil.
I've also seen them fall right over from the same shot so I'm not condemning any caliber.