Alright, not sure if you've made your own ruleset and stuff for this, but I'm writing this purely as an intellectual exercise.
Ayakashi are beings that thrive on Fear of mortals and gains them by spreading their Legend, such as, as you wrote once, the museum Youkai that is capable of creating illusions and phantasmal-looking flames, through spreading the Legend of a museum that causes people to disappear on Thursday evenings (?), and when coming out (on Tuesdays), they said that they were chased through an endless corridor.
This is but an example of how they're capable of getting stronger, through spreading their Legends.
In Highschool DxD, they're also said to be capable of naturally learning Senjutsu, and for the more physical ones, Touki-based skills, not to mention their own variants of Youjutsu, though the lattermost skill, is restricted to the type of Youkai practicing it. For example, a pure-blooded Nekomata/Nekoshou is more or less incapable of learning Frost-based Youjutsu, but it is possible for them, albeit more difficult, to learn it through hard work or some other cheats, such as reincarnation into a Devil via the Evil Piece system.
Youkai, when born/conceived/created/???, have an effective Essence rating of 1 or 2, or in the case of Youkai whose parents are sufficiently strong enough, such as Nurarihyon, or leaders of the Hyakki Yako, the Youkai child's starting Essence would be higher, at most, estimated to be at 4 or 5.
To gain Exp or raise their Essence, Ayakashi must spread their Legends associated with them over an area they have claimed as their territory, thus gaining the fear/respect of mortals that allow them to become stronger. The same applies to them if they were to raise their Epic Attributes, though they'll have to be more creative in the spreading of their Legend if they were to raise/learn an Epic Attribute that is not associated with their particular Youkai species. Examples include, say...a Physical-based Fear user who wants to gain Epic-Charisma, which would require him to learn how to use Presence-based Fear techniques, thus requiring him to add something that affirms the Presence-based Fear aspect in his Legend.
...
Onis have a better time learning Presence and Physical Fear techniques.
On the subject of mote recovery and calculating total motes of Ayakashi, treat as if they have a new Background rating of Fear, of 1~5 (and N/A) rating, that acts as Cult rating when calculating mote recovery, and similar to Terrestrial Exalts' Breeding rating.
1 dot - Increases mote pool by Essence/2 rounded down +2, increases mote recovery by 3 motes every day/night.
2 dot - Increases mote pool by Essence/2 rounded down +4, increases mote recovery by 5 motes every day/night.
3 dot - Increases mote pool by Essence/2 rounded down +6, increases mote recovery by 7 motes every day/night, +1 Willpower recovery every day/night.
4 dot - Increases mote pool by Essence +8, increases mote recovery by 9 motes every 12 hours, +3 WP recovery every day/night.
5 dot - Increases mote pool by Essence +10, increases mote recovery by 11 motes every 6 hours, +5 WP recovery every 12 hours.
N/A - Increases mote pool by Essence*2 +20, increases mote recovery by 15 motes every minute, +7 WP recovery every 6 hours.
Please note that the above is generic Youkai template. There're other kind of Fear ratings as Background, depending on the Youkai in question, which requires some kind of condition to be fulfilled. For Water based Fear users, they could gain the bonuses noted above when underwater, or in close vicinity to a water source. Furthermore, the more...restrictive the Fear condition is, the more potent the bonus are.
And the N/A is reserved for Ayakashi who somehow gained enough respect/fear from other Ayakashi that they ascended into divinity. I, for one, won't be surprised if said being manages to gather what I tentatively dub the Night Parade of Eighty Million Demons, aka uniting every single Youkai under his/her banner.
Yukari Yakumo comes close when she gathered a Hyakki Yako during her Moon Invasion, but it disbanded during its failure. Assuming that the title of Youkai Sage is not an exaggeration in your quest...she may very well have a mastery of Senjutsu, Youjutsu (which involves Displacement and Creation based Fear techniques, and in her early days, Presence based Fear, in which she hadn't used in centuries, I must wager), as well as Omyoudou. Wouldn't be surprised if she's described as a Super Youkai in the modern world, due to how bullshit her powers are.
...Ugh, now I'm rambling. But still, thoughts?
