Unfortunately, two extremes don't make a happy medium. Yes, the glazed pot was probably a bad idea, and soggy soil doesn't sound good either. I think you need to raise humidity but keep the rooting medium aerated.

Fuchsias don't have stolons. Phygelius, which are often mistaken for Fuchsias, do. Fuchsias do root so readily that low-growing branches often take root; that is fairly normal; I don't think that counts as a true "stolon" tho. I'm not sure but I think they are capable of root-suckering too. I've had vegetative offsets mysteriously show up next to other plants, usually from broken branches but sometimes I suspect from me digging around the roots.

Unless you are close to the Pacific (especially if you are in southern California) this does not seem like a good time of year to start Fuchsias, except possibly the heat-loving triphylla types like Gartenmeister Bonstedt (that's "Gartenmeister's" full name). Try to find as cool a spot as you can. If it is G. Bonstedt, try it again if she doesn't mind. One possibility are gel rooting mediums. Those are supposed to work well with Fuchsias (and apparently not so much other things), and they'll keep it hydrated. Oddly enough, gels or for that matter straight water are better aerated than soggy soil! Make sure the starts are kept in a SHADY location, like the north side of the house, and because California's humidity is generally quite low I think you'll need something like a coldframe or other form of protection to raise humidity.

To answer your question your start isn't necessarily beyond hope. I always worry when they lose their only leaves but I've certainly had bare twigs root! Fuchsias WANT to root.

Good luck and I hope it works out one way or another.

Atash,
Thanks for responding. I looked up Phygelius & it's not it. It's flowers are hanging not on a stem & the leaves aren't veined red & red underneath like tlhis plant is. The cuttings are looking like they might be recovering & I've moved them into full shade (one is inside). I think this may have just been a really bad week to try to do cuttings. We're having very dry "Santa Ana" winds so it's much hotter & drier than usual. I'll have to look into the gel rooting mediums. It's encouraging to learn that fuchsias want to root!
I'll let you know how it works out.
Traci