For option 2, Cel'n'Cur aren't the brightest buttons in the box, so no, they wouldn't have brought gloves. As far as they're concerned, they have an absolute right to hold the Silmarils, so 'maybe they'll burn us' isn't even on their radar.
Option 3... option 3 is interesting. ^_^
Feanor trapped in the Silmarilli makes, uh, 'sense'; he's literally named Firesoul, and the things were designed to capture light. But how would he respond to being wished at?
Let's assume he's arbitrarily powerful at this point. He's had nearly 500 years of sitting around on Morgoth's head to hone his post-mortal artisan skills, I'm sure he can craft a spiritual invention for every occasion. And rather than a literal 'has to do what you say' (in which case Morgoth would already have used him), a 'will do pretty much anything to get away from Morgoth' rule will function in much the same way, but still let him argue.
To hew a little close to Aladdin canon, the first 'wish' could be the whole 'I bet you couldn't get us four out of here'. That puts the gang outside Angband, where there's a rather angry wolf hanging around.
Hmm... what if the quartet appear in hiding, and it's Cel'n'Cur fighting with a) the lovers, b) their ghost-dad, and c) each other that attract Carcharoth. Then Aladdin gets his hand chomped (losing one of the three Silmarils), and Jasmine makes a wish on his behalf - 'he wishes for you to get us away from everyone trying to kill us!' That matches Aladdin's second wish, and also gets around the eagle situation.
Feanor has to leave Cel'n'Cur behind (because they're part of the 'trying to kill us'), which means Aladdin can do his 'make me a prince' wish in relative peace. That runs him out of wishes, because the third one is locked in Carcharoth's belly.
So now we're in Doriath, and Sultan Thingol hears of a great wolf on the rampage - and two elven hunters chasing it. Cel'n'Cur wouldn't let the one Silmaril left near them get away, right? All three of them are heading for Doriath.
So as Carcharoth romps through the forest, Cel'n'Cur go and steal the remaining two Silmarils from Aladdin. That's when they pull Jafar's 'make me Sultan/make me as powerful as Sauron' thing (and also a 'make Jasmine love me', which is actually a thing Curufin wanted in one of the early versions of the LoL). Aladdin points out that Feanor is still more powerful than them - but that they're out of wishes. Which means all four of them (plus Huan the Tigerdog) get to go hunt Carcharoth.
If Feanor is a ghost, do Cel'n'Cur get mortally wounded during the hunt, take the Silmaril between them, wish to 'be just like you, dad', and then promptly die? If you want a happy ending, Beren can't die, so they can take that role. That leaves Aladdin free to take up the last Silmaril and set Feanor free at last, to go (with his sons!) off into the West and seek some kind of rest.
Obviously that's just one option, but I think it shows that it could work.
~
Now: what would this do to Arda? First off, you'd very shortly have a Sudden Flame 2.0 as Morgoth comes stomping out (not in person, his feet hurt) to try and get the Silmarils back. I'm trying to get my head round how that war would play out - on the Elves' side, they aren't at all ready for it, and are still reeling from the last one, but Morgoth isn't prepared either, and he doesn't have a traitor in Maedhros' camp like he did at the Unnumbered Tears. With the Host of Angband heading straight for him, Thingol would have to actually send his army out, and between him, Orodreth, Turgon, and Fingon, I think they could pretty much destroy anything Morgoth sends down the Vale of Sirion.
The east is a different matter. If Morgoth goes that way, the (remaining) Sons of Feanor are going to be pretty battered, and have to withdraw. So in a reverse of the canon, it's going to be East Beleriand which is overrun, with the dwarves, the Green Elves, and Maedhros fighting a guerilla war, while over in the west, things are relatively okay.
Once that's resolved, Maedhros now has a huge grudge against Doriath. Not only do they have all the Silmarils, they also killed (kinda) two of his brothers. In canon, he leaves them be until Luthien dies; I don't think he'd do the same here. So you get an attempted Second Kinslaying against a Doriath led by Thingol, Melian, Beren, and Luthien (since they didn't die and wander off to Ossiriand). Again, I have no idea how that would go, but it would be super messy - and of course, with the Feanorians focussed on Doriath, Morgoth would be able to push through their remnant territory and cut around to the south...
Yeah, I have no idea where this ends up. Earendil crossing the Helcaraxe? Luthien and Melian taking on Morgoth face-to-face? Maedhros making common cause with Angband? Pretty much anything could happen!
hS