Spellspeed and piety go hand in hand. More spellspeed, more piety required. You'll also need a lot of spellspeed to get to breakpoints where you simply forsake a Benefic 2 in favor of two quick Benefics. Due to how scripted things are and how little spellspeed affects HoTs, it is a reliable stat but very breakpoint based for an AST. Spellspeed also doesn't benefit any of your ability heals (Essential Dignity, Collective Unconsciousness(not sure if HoT factor does benefit), Retrogradation(PvP)).

I'm fairly sure Crit is the stat that increases HPS the most but also the most unreliable for clutch healing. It will balance out on HoT effects pretty nicely to the amount of times they tick in a fight, and if you are aware of the situation a crit heal will give you breathing room a normal heal wouldn't give you.

Det is the easy option. Just flat-out increases healing, no strings attached.

Really, every healer seems to take a different combination, but in general you'll need more piety if you go spellspeed (unless you hit efficiency breakpoints, like the Benefic 2 vs 2 Benefics example) and crit tends to give bigger HPS values in the long run, albeit random. If you happen to fish for crits as Nocturnal (because waiting for big buster, anxiety, whatever) for big shields, crit will naturally be more favorable. too.

Personally, I go crit = det > sps, slightly favoring crit depending on whether I have to DPS a lot and there being a DRG in the party. I'm fairly sure crit provides the best HPS boost for both sects over the duration of the fight, just not always when you want it to. But meh, I didn't go AST because I wanted to be 100% reliable and predictable anyway.