6.5/.264 projectiles are not ideal for large game. The properties that make .264's excellent for long range shooting (high BC's) inversely affects their effectiveness on game (high SD's). A high sectional density means the projectile will have a high degree of penetration, which on the surface this seems desirable, however if the bullet fails to expand (which a long narrow bullet will), it will pass through the target. If the shot is not well placed, the bullet will not cause sufficient trauma to immobilize or kill the target. Elk are very tough, and even when poorly hit with larger calibers, they survive. So the irony is that given the milder recoil, shootability, and great long range characteristics of a 6.5, you have a higher likelihood of hitting an animal at long range, however it is less likely that your shot will be lethal, unless both your projectile and shot are well chosen.
Regarding projectiles, if you insist on doing this, you want a bonded style bullet that will not fragment if your shot is close and energy/velocity are high, or fail to expand if your energy/velocity are low. The Nosler Partition/Accubond, Federal Terminal Ascent, Sako Gamehead/Hammerhead/Superhammerhead, Norma Bondstrike, Swift A-Frame, Hornady Interbond are effective hunting bullets at most ranges.
Frangible bullets, such as Hornady ELD-X/ELD-M or Bergers are effective if the shot is placed in the lungs/organs. They are not effective if placed in hard/dense areas where the bullet will expand/explode without much penetration.
Monolith bullets, such as Hornady CX or Barnes TSX/TTSX/LRX are the opposite of frangibles and require resistance to force them to expand, so ribcage shots that miss the lungs are not good as the bullet will pass through with little trauma. Shoulder shots are much better as the bullet will break bone and continue to petal and cause trauma until the bullet runs out of energy.
A 7mm or 30cal would be much more ethical if you insist on shooting elk at those distances.