A few things I've noticed:

1. It seems that your desynth chances go up by exactly 1.5% per level. It seems like there's an initial chance for each ilvl (which might be negative), and your desynth success rate is (InitChance+(1.5%*DesynthLvl)).

2. Desynthing gives massively diminishing returns for experience. At level ~70 skill, I have a ~77% chance to desynth ilvl 55 items and I only get ~0.05 experience from them.

3. ilvl ?-49 items can give 1-2 non-clear Demimateria I and clear Demimateria I-II. ilvl 55 items can give 1-2 Demimateria II. Chance of non-clear Demimateria seems to be about 10%?

4. When DoW/DoM items give non-clear Demimateria, it's always Battlecraft. When DoL/DoH items give non-clear Demimateria, it's always Fieldcraft.

5. Since ilvl 55 DoL/DoH items do not give Fieldcraft Demimateria III, the only items left that can give Fieldcraft Demimateria III are the Artisan Tools/Spectacles and the Foragers Tools/Hat. At 100 skill, you will only have a ~95% chance (I forget the exact number) of success desynthing these items. If the pattern holds, you'll only have a 10% chance of getting the Fieldcraft Demimateria III. That means, to get the 10 Fieldcraft Demimateria IIIs needed for one new upgraded tool, you'll have to desynth about 105 Artisan/Foragers items. The cheapest way to do this is to use Artisan Spectacles (GSM desynth), which cost 10 HQ Spicy Tomato Relish each. So, you'll need about 1052 HQ Spicy Tomato Relish to get EACH new primary tool, which is 11,579 HQ Spicy Tomato Relish for all 11. Look forward to it!

6. If my math is right, you'll have a 100% chance to desynth Ifrit's Cudgel at 93 skill, which isn't that bad. It's really bad for Mog weapons though, since you can never hit 100% desynth for them.