The kicking part was the radical jump. Our guild did exactly what you mentioned. We had two under performers, they have been under performers for years and for the most part we were always able to carry them. Come T14, those days were over. Those two people would regular get beat by the tanks on fights like the 4 kings and Blade Lord, Garalon. They were both range and any fight that required movement they stunk. So much that we simple couldn't get past fights like Garalon or Elegon if they were in raid. They got sat, we progressed great. We had alts raids to help them play and get some gear, but gear was never the issue. At one point one of them was our best geared person and still lost to the tank, normally doing 20-30k less than everyone else.
These aren't barriers of our own creation. I raided on an Alt with a guild that is still 2/12 and it takes about 5 or 6 wipes each week to get Horridon down. They knew exactly the strat to do, but heals, tanks, DPS just couldn't execute. And they are down to pugging 2-3 spots each week, because they can't find anyone who wants to raid 2 nights a week, I suspect eventually they will get tired of farming 2 bosses and just quit raiding.
So what options are really there besides
1) recruit more people fill slots or better people to take the place of slackers (on a server that is dying off like some many server now)
2) go back to the previous tier for better gear (2 months after the newest tier is released and LFR gives better loot)
3) abandon normal mode raiding all together (accept raiding isn't for you and call it)