I'm confident I'll be on the opposite side of most responses to the OP's question.
For example I'm at 9,000 ft and run a 7mm 08 with a 162 ELDM at 2700+ fps out of a 26" braked bartlien barrel. It has and will crush elk out to 900 yards. (ok crush is a bit strong lol) Not because it's a beast of a cartridge but because the 7mm ELDM bullet will perform down to around 1800fps even a bit slower. In the same breath I'd be cautious to run a traditional 140 gr anything past 350ish yards in a 7mm 08 just my opinion.
My first take away to the OP is... match the "bullet" with the velocity it needs to be moving to perform at the distance(s) you are considering. Manufacturers' list the min velocity necessary for their particular bullet to perform so you can match your shooting distances to the cartridge size needed and MV necessary to reach that result in a given bullet size. Funny thing is that does not always equate to a beast of a magnum even at 1K.
For example, most will agree Hornady says the 162 ELDM needs a min of 1800 FPS at impact to perform as designed. I reach that threshold, at or just under, one thousand yards. Where as say a faster 7mm - a 28 Nosler will hit the 1800fps threshold a few hundred yards further say 1200 yards or so - don't quote me but confirm. However, to do that you have more recoil with higher MV, throat wear, cost per shot, etc with the same bullet. If you change bullets then all is lost and we have to start over lol.
An interesting side note: I've had lots of shooters (experienced and not) that run the fast 30's, 7mm, 33's etc get behind that 7mm08 and can't believe they are able to get first round hits out at 1270 1400, 1760, 2260. Every time - I see a light bulb go off in their head and a grin on their face. Hell I run that rig in PRS comps too. For some reason even experienced shooters associate distance with bigger calibers and more recoil.
Another take away if anyone is still reading lol. Since 900 yards is good shot for anyone on game regardless of a given MV. I'd personally rather do it with less recoil. That is not to say I don't like running my 338 Edge because I still do.
Another source to help the OP decide on a caliber to drive 7mm or 6.5 bullets is to look up Nate Foster in New Zealand. He has done and continues to do extensive research dissecting animals killed in the field and clearly demonstrates the results that a given bullet and cartridge case size produce at given ranges. Super insightful and based on facts not theory or opinion.
**let us all know what case you decide on ... to drive your 7mm or 6.5 bullets!