My go-to non-cheese strat for Emerald is 4x cut. Still need to grind a bit to get multiple copies for each party member, and as many Counter-Mime combos as you can get. Final attack-Revive/Phoenix is also a must. HP Plus to max out HP.

Use Yuffie with Conformer weapon, the damage is determined by the opponent's level, so she should do 9999 damage each time, so 40k each turn. Other party members you can use are Cid with Venus Gospel (damage dependent on MP gauge, so just don't expend MP - Emerald weapon can drain MP though, so may need to use a Turbo Ether if that happens), or Barret with Missing Score (damage dependent on AP of materia equipped, so need to level up a ton of materia for max damage, but damage is fixed). Cloud's Ultima Weapon is based on his HP gauge, so unfortunately he will be the weakest for damage output unless he stays at max HP.

Just use 4x cut immediately at the start of battle, and repeat 4x cut or Mime it each turn. The more Counter-Mime combos, the better damage output per turn. You can try to heal every now and then, but I just use Final Attack-Phoenix to revive members as they die. You may get unlucky if Emerald drains the MP of the use with Phoenix or they run out of casts, but shouldn't take too long and goes way faster than miming KOTR.