I did some more testing with MND and WD. I found that MND is slightly more powerful than my thoughts above. These are my preliminary stat weights.
WD: 3.0
MND: 1.0
CRIT 0.25
SpS: 0.30 - I just realized I used 100 SpS, but 200 CRIT and 200 DET in my calcs. I've updated this number
DET: 0.08
I place PIE at around 0.2, slightly above SPS, below CRIT. These stat weights are excluding the CRIT benefits of SCH's adlo and the SpS downsides of SCH's fairy (so mostly WHM/AST). I am willing to accept that DET may be slightly higher, but not a lot. I'd say maybe 0.12 or so max. My testing was minimal, and the increase that DET (6.9) gave was well below the standard deviation of heals (55)
I did some minor CRIT testing as well - with only my book equipped (100ish crit) i had a 1.5x modifier as expected. With all my gear, I had a 1.55x modifier (840 CRIT). It's hard to tell if this was within the normal fluctuation, or if that is a 0.05 added on with +500 crit. Either way that seems quite a bit lower than I expected of 200 crit for 0.05 added
EDIT: Working out some SCH stat weights
These stat weights are tricky as it depends on the scholar, usage of pets and usage of adlo - but here goes.
Spell Speed
This will affect each pet differently. I have a log with Eos doing 47% of my healing, but I would say she is far closer to 30% on average. This depends heavily on Whispering Dawn usage (where Embrace is roughly 20% and Whispering Dawn in that log was 27%). Selene would, in that sense, be 20% of a SCH's healing. Again, this is dependent on content etc (in expert roulette, pets are probably more like 80%). Spell speed does not affect pet cast or recast time. I am unsure if it actually helps the potency on whispering dawn either - but as usage of this skill is limited and the potency amount is negligible, I am going to leave it out.
In this sense, the calculation is the same however:
Eos: Stat weight x 0.70 = 0.296 x 0.7 = 0.20
Selene: Stat weight x 0.80 = 0.296 x 0.8 = 0.24
CRIT
This one is tricky, because it only changes with Adlo and no other heals. According to several different logs, adlo takes up 1.6% of my heals in Seph, 5.5% in A5S, 10% of my heals in Expert roulette. For the sake of argument, I am going to say Adlo = 6% of heals.
Therefore the calculation for the stat weight is:
Chance x Impact x Portion of healing
(0.05 x .5 x 0.96) + (0.05 x 3 x 0.04) = 0.03 = 3% = 0.30 stat weight; however, there is the added benefit that procs on your pet increase your SpS. I don't have a lot of hard data for this, but I'd expect this to not be a very significant increase
SCH estimated stat weights:
WD: 3.0
MND: 1.0
CRIT 0.30
SpS: 0.20 or 0.24
DET: 0.08