Summoner Question: Where should I spend my Myth tomes first?

[T0rin]

Well getting Myth belt was a mistake.

Not really, Myth belt, while being slightly less damage than Allagan belt, actually turns out to be BiS because it has Accuracy that SMN need to hit the Garuda accuracy cap. If you got all 'pure damage' pieces, you would end up with something like 428 accuracy, which you could augment to ~432 with food, but your Garuda accuracy would be crappy.

I read somewhere it is worth to have full acc set on summoning then switch to INT-Crit-Det once the Summon is up, even when it shows it updates over time but in a LONG time.

It also updates when various buffs are cast on the pet, i.e. Rouse, Fey Covenant, and who knows how many other spells. Relying on an alternate set used when summoning is just not reliable over time. You either go accuracy for the pet full time, or you accept sub-par accuracy on the pet for Coils. (and future content)