It's quite funny that it's taken all of this math for a lot of you to agree that doing what you want with secondaries is perfectly valid. Healing has never been about HPS, so trying to min-max your secondaries is somewhat frivolous. We care more about preparedness, pre-casting, and snappy responses than we do about HPS.
This is why I personally think that White Mage's should build Spell Speed. Yes, Crit is in fact "optimal" from an HPS perspective, but as others have said most of that increased HPS is going to end up dumped into the overheal percentages. If you try to top your tank off at 80% and score a Critical Heal then all you've achieved is overheal. That doesn't really help anyone. There is something to be said about the benefits healing after a tank-buster, but I can't imagine that you would get entirely too many criticals at that exact moment compared to all of the other random times you might instead. A lot of what I'm saying probably applies to Diurnal Astrologian too, but I'm no expert on the class and won't try to speak for them.
Spell Speed on the other hand has one extremely significant advantage over Crit. See, White Mage as well know by now is a "reactive" Healer. That label is somewhat misleading because you should always try to precast, but with White Mage you need your cast to land AFTER the tank buster goes off. Although large amounts of spell speed will make the timing window a bit tighter, it also means that you're less likely to be in the middle of a cast when the tank buster starts, and it also means you'll be able to react faster once the damage goes off. Couple this feat with that fact that SpS still increases your HoT and DoT ticks and I say we've got a winner. The Synergy here is good, even if it might not be the best for HPS.
Scholar on the other hand has no business trying to play with Spell Speed. We synergize entirely too well with Criticals. Adloquium alone makes stacking Crit permanently worthwhile for Scholars, but the fact that shields can never be "overhealed" means that Crit is still worthwhile for moves like Succor. Doubly so since Succor's low potency can be kind of disappointing unless it crits. As if it all wasn't enough already, Fairy Crits gives us a Spell Speed buff anyway, and Selene grants everyone Haste.
As for armor Melds. Accuracy all the way. Scholar's aren't Healer's anymore, and we don't get free accuracy on our gear. We need every point we can get. Maybe Vitality while you're still gearing up, and maybe Piety if you're a White Mage.