I wonder which mountain's peak likely has the higher elevation above sea level, the Caradhras (highest mountain of the Misty Mountains, located above Khazad-Dûm) or the Eilenaer/Halifirien (at the border between Rohan and Gondor, highest of the seven beacon mountains, probably highest mountain of Rohan and among the highest peaks in Gondor and the Ered Nimrais).
Both mountains are covered in snow so that both peaks must be higher than 8,000 ft (snow line at midlatitudes) while on Eilenaer there's the beacon patrol so its peak must be low enough that hypoxia is no issue (reportedly 75% of climbers experience altitude sickness above 10,000 ft, and I guess the patrol exchanges once in a while). Therefore I'd rather go with Caradhras, and the Caradhras actually looks higher to me seen from Eregion than the Halifirien seen from Edoras though we don't know how high the plains of Rohan are above sea level.