I think the pros and cons are pretty obvious. You are said its hard for you to find the time to waste a GCD, but you have no problem finding 10 seconds to channel? It doesn't make sense to me, but whatever works.
During heavy damage times, the value of a GCD is more important than during low damage times. Finding time to burn mana tea stacks when their is low damage is easy. I typically do this in between cooldowns of my renewing mists.
The other part of my comment is about you using multiple surging mists on the same target without a clearcasting proc. I don't think its a good practice, so it makes me skeptical about some of the other things you might be doing.
Glyphed Surging Mist removes the target requirement, so you aren't casting it on the same target.
In addition, I think it's the fact you have twice the Spirit as Suplift and Somurd have. Yeah, that sounds a lot more like it.
Spirit would have to enable me to go longer periods of without relying on mana tea. Even with that amount of spirit difference, I still feel that the mana costs that would be required for burst healing wouldn't account for spirit regen. In short, when we use mana, we use a lot of mana in a short amount of time.
glyph doesn't take you out of the healing and returns the same amount of mana. If you're good, you don't fall behind. You can continue to heal and can continue to damage without losing anything at all.
1 GCD > 5-10 seconds of channeling.
1 GCD during heavy damage < 5-10 seconds of channeling during low damage. And you are actually comparing a GCD (1.5 seconds) vs 2 seconds channeling, which is no where near 5-10 seconds, for the same amount of return.
If I can go through a heavy damage phase without needing to waste GCD's on Mana Tea, it will result in more healing throughput given that I have a sufficient time available in a lower damage period to get mana back.
If I have to use a GCD throughout this time in order to keep my mana pool up, then it will be a net loss in healing during the heavy damage period.
The other option is to fall behind in using your mana tea stacks during heavy damage periods, but at the given rate of mana return, it may not depreciate your healing or mana pool.
The only situations where I would want the glyph would be in soft enrage situations where damage progressively gets stronger since you wouldn't have that down time to get your mana back. Although in the previous expansions, it was still possible to do this as a holy paladin and not detract from the overall raid healing.