The 'temporary power'-based healing method I mentioned (option 4) was something that occurred to me while drafting the first post above, and I've been mulling it over. Perhaps it would work something like this:
1) You'd need a caster with the appropriate magic. Seelie magic or Biomancy, possibly requiring that the Biomancer meets some minimal skill qualifications as Mr. Death suggests.
2) The caster would cast an appropriate spell to grant access to loaned Recovery of the level desired. In addition, he'd need to supply enough duration for the spell to last as long as the consequences would normally require to heal without the spell. (Note: without this odd duration rule, there would be no reason not to simply borrow Mythic Recovery until the next scene over borrowing a lesser Recovery for longer.)
3) The target spends a Fate for each refresh worth of borrowed Recovery. The character's refresh is reduced as appropriate until the spell expires. This refresh penalty does not cause the character to 'go negative', and it is returned once the spell expires or is ended prematurely, though the Fate points would not be returned until the next refresh period after.
4) The borrowed Recovery only applies to the consequences healed, not to any new consequences earned later.
5) If the spell ends prematurely (due to a dispel, for example), then the the character's consequences revert to whatever they would have been if normal healing had occurred.
For example, a character takes a mild, moderate, and serious consequence. A Sidhe generously casts a spell to grant him Supernatural Recovery ... for a consideration to be determined later.
Normal healing would have resulted in the mild disappearing after one full scene (about an hour), the moderate disappearing about a full session (a few days), and the serious drops off after a full scenario (about a month). Supernatural Recovery would result in the mild disappearing immediately and the moderate disappearing before the next scene (15 minutes?), with the serious lasting merely a full scene (about an hour). The Fae needs to cast the spell to last the full month, and the healed character gains the benefits of that healing as if he had the Recovery power. However, if an ebil Sorcerer detects the spell and dispels it during the next session (or a week later), then the player gets the serious consequence back (with a session or a week credited toward recovery). The mild and moderate stay healed, since they would have healed by then anyway.
Note: if a character has to 'regain' a consequence that he currently has marked off (because he's recently taking more damage), then he must (a) mark off a number of shifts worth of consequences to match the regained consequence, or (b) roll the consequence up into the next available consequence, or (c) be taken out (as if by the dispelling character).
It's a work in progress, clearly. Requires some book-keeping, though of roughly the same degree that the original consequences would have required. For tracking purposes, you could just replace each consequence with a 'virtual' consequence (that would have no game effects) as the Recovery power healed them. These virtual consequences would go away for good when the consequence they represent would normally have healed without the Recovery power, or would become 'real' consequences if the spell was cancelled.