HOORAY! Update!
I'm changing my style right now. If I do the same analysis, it might get more than one person killed. Though, it was fun to see.
Common sense stuff
-First off, besides trading cloth and sunshine to dwarfs, elves are good for only one other thing. Dying, what else are they going to do with their infinite life span?
----With that first thought in mind, I say we either shoot the winy elf where he stands or dump him in the booze to feed him to the titan. Or we could do both!
-This is a titan. His needs are obviously larger than that of a normal elf, dwarf or human. He will need alot of booze to get drunk enough for us to trick into leading into a cage. Let's ze, on average the volume of the human stomach is a little over one gallon, so 1.10 gallons (4.16 liters). That said the average dwarf drinks at least three to two times a month in fortress mode (the same goes for elves and humans). Since this is basically that, I'd say that this Titan needs at least six units of booze (a frog's stomach is fairly similar to ours) to feel hydrated and on average a barrel of booze carried by all caravans carries twenty-five units of alcohol.
----Since these elves have been represented so far as a bunch of pot smoking happy go lucky suicidal insane idiots, I'll go on a limb and say that their stuff if pretty hard shit. One barrel of booze and a few decent herbs (and a drugged elf) should be enough for the titan to get decently hammered, one and a half for good measure.
-Course, if we leave the titan in a cage we lose a decent body guard.
My Diplomatic approach.
20 mules
2 caged elephants
1 caged dead elephant
4 caged hoary marmots
60 barrels of strawberry wine
58 Barrels of Strawberry win
10 bundles of rope reed cloth
10 baskets of various berries
10 bins of wooden goods
10 barrels of assorted herbs (cooking herbs included)
10 of the highest quality rope reed blankets
10 spindles of rope reed rope
8 bundles of wood blessed by the druids, (2 had been converted into cages)
9 bags of provisions (dried fruits and seeds)
We agree with the titan to stop singing and give him two barrels of booze to spare our caravan. One to sip and one to keep before he goes back to sleep. We also say that if he guides us to the edge of the swamp we will give him an extra barrel of booze with the selling line that it will "Condense his entire million years of life into the single moment when he has a sip of this booze." We secretly roofie his drink on the way and don't forget to put as many delicious edibles into it on the way.
If we make it to the end, we should hand him his barrel of booze and state "that the drink will go flat if he doesn't drink every last drop of it in the next ten minutes." We
slowly and discreetly back from him as he has the last few drinks. After he falls to the ground, we
hurry the hell up to get him into a cage. One of the elephants should help, say that the titan will burn us all alive if he isn't in a cage to get the elephant to work. After that is all said and done, we make up a good story to explain how we dealt with the titan to Amala. With the story specifically mentioning that Amala did not get hit by the titan. I don't want to see her kill a perfectly good titan.
[etc][etc]
You are thinking waaaaaaay too much in long terms.