Getting trained has always been an issue with restoration shamans. Even in their peak of overpowered popularity (S11), 3DPS teams were notorious for climbing the ladders simply by opening and tunneling the resto shaman and hardcountering RLS comps because they couldn't actually peel or land a cross kill fast enough (usually) before their shaman died.
In reality, it's going to mostly be about your partners peeling for you. Either through literal peels, with crowd controls and the like, or through making the other team go defensive somehow (blowing up their healer or dps etc).
You need to remember that cleave teams usually blow everything at the start, so don't be afraid to use all your cooldowns. Your DPS also really need to pick a stance: either they need to peel and try to find a chain that they can kill someone in, or they need to also go balls to the wall and attempt to get a kill and peel by forcing the other team defensive.
Resto shamans have the tools to live for a long time with SLT, Aura Mastery, Healing Tide, and NS rotations. You just need your teammates to end the game before you run out of them. Monk teams are especially good versus this, because Ring can by itself ruin a thug cleave opener or a feral popping beserk if they successfully get it off and adds another cooldown so your NS comes back up again.
In short, just pop everything and race them, especially as DK/WW/Rsham. You have the tools to outcleave their cleave as DK/WW can do insane amount of healer pressure in a short amount of time. Have them toss a casual Ring of Peace on you and hope that your two melee can kill their healer before their melee kill you.
As sad as that sounds, that's cleave vs cleave in a nutshell. Sorry I can't really go into any specifics, because it doesn't really sound like you're doing anything wrong, and this problem isn't exclusive to lower rated healers; players like Cdew get cleaved down without much they can do as well.