My last Primordius kill I did around 90k hps with a resto shaman, resto druid, and prot pally (they do insane amounts of healing right now). I would have expected your pally to be higher due to the higher gear level compared to me (543 vs 539) and the fact that you were 2 healing it.
Spirit is a tricky thing because it may not make mathematical sense to take the spirit flask over the int flask, but you need spirit in order to sustain healing, and that depends on the fight and your healing rotation. Are you using a mana-efficient or mana-inefficient rotation? Are you tank healing or raid healing? Is it possible to melee to get mana back via Seal of Insight? How much running around do you need to do? The healers need to ask the question "Am I running out of mana?" If so, why? Legitimately healing hard? Spirit flask makes sense here, especially on progression. Just messing up or using the incorrect rotation? Flasks won't save you there...someone needs to fix what they're doing.
If you need the regen, take the spirit flask. Otherwise, use the int flask. It's not cut and dry like DPS and tanks.
For reference, I've had shitty luck with trinkets and I would happily drop my spirit trinket for Lightning-Imbued Challice or (more preferably) Horridon's trink. 14k unbuffed with 33% mastery (also had bad luck with healing plate drops, so about half of my pieces are haste/spirit). If you have Horridon's trink, 12k should be a reasonable amount of spirit to have. The trinket proc is about equal to the spirit trinkets of the tier, usually more, and provides better throughput stats. If it ever drops for me, I might reconsider switching to int flasks.