I have had animals test positive for coccidia twice, both animals were male and both are doing just fine now. Neither were sikorae though- one was sameiti and the other henkeli. Both were prescribed the same thing you were- albon administered orally. Cricket is correct that it can be very hard on them if they're dehydrated, so you need to make sure that's not an issue before going through the round of albon. It shouldn't be a problem nose dropping water or pedialyte on the animal, and I've had good luck getting a lot of liquids into them that way. You just have to be patient and wait until they're licking. If he's severely dehydrated, you can take him in to get subcutaneous fluids... sounds complex but there's really nothing to it. You can do it yourself with the right gear and if you're comfortable/careful. I know my own vet, and let them work on my Uroplatus, but realize that most vets have never seen one and might just kill it themselves. Developing a good relationship with a qualified vet is a must for keeping Uros, IMO.
I'd keep up the soaking, nose drop lots of liquids and/or see about the subQ fluids. Once he's decently hydrated, drug away. Coccidia will kill him if you don't, so don't mess around. I'd also mush up some crickets or even CGD and try to get something in his system. Coccidia destroys the gut lining, making nutrient absorption difficult. That's why they regurge, but if you can get some nutrition into him that is in liquid form he might be able to utilize it.
Also, if you can get them into a very simple setup, housed alone preferrably that would be great. That way you can monitor if they poop/regurge and who does it. Meanwhile, you can nuke the current tank. Coccidia oocysts can remain viable for up to 6 months, and it's nearly impossible to eradicate but that doesn't mean you shouldn't try. 10% bleach mixture, steam, ammonia... (just don't mix them)
throw away the furnishings and substrate and re-do everything. Treat is like it's ebola for geckos.
I'd be interested to hear how they do, please update.
EDIT: After re-reading your initial post, I forgot to address one of your concerns- I've had all manner of medical wierdness in my Uroplatus collection, and have had to handle mine many times. I've never seen anything that leads me to believe they suffer any long term affects from being man-handled when necessary. Heck, they don't even seem to be affected short-term. I think that's a total myth/assumption that comes from their reputation for being a fragile genus. I've picked up, squeezed, gotten them to gape at me, dosed, force fed etc. only when I've needed to, but I've had plenty of animals eat that same night and seen no difference at all in them an hour later. Long story short- do what you have to do to get fluids, nutrients and the albon into that gecko.