Just my opinion, but I think the minuses of manhandling a big bike around that part of the world far outweigh the pluses. Unless you're the masochistic type, or maybe an attention seeker who thrives on the whole celebrity thing - an inevitable consequence of rocking up to a third world village on something worth more than a local house.
I know 99% of the locals ride bikes under 250cc simply because they can't afford anything else. But the other side of it is that they're far more practical in most situations and on most roads. Some of the scariest moments of my life have been riding big bikes on and off various boats, or over diabolical roads in SE Asia.
We've been hanging out near Penang for a while, and every time I take the Dakar out for a blast through the rice paddies, or some of the twisty mountain roads near Thailand, I think what a perfect bike this is for around here. A few weeks ago we did 1000ks into Thailand, and again the BMs were great. But for the places you're talking about, bikes like this are just a huge pain in the ass IMO.
By a cheap local 125. Who cares if it breaks down. Anyone can fix it. Who cares if some idiot in a Hilux totals it. At most you've blown a couple of grand. So what if the road turns to shit. Some of these little 125s are supreme off-road machines. And because they're much easier to ride, you're gonna have a lot more fun doing it.
I can't really comment on the paperwork thing, other than to say we've used carnets all through this region. There's some garbage floating around these forums relating to Indonesia and carnets, but if you're determined to import your own bike you'll need one. Indo customs expect one, so you'll be at their mercy otherwise. But who knows if you're bringing in a Thai registered 125? You'll be a bit of novelty for sure, but I'm guessing the fee to import it will be a helluva lot lower than if it was a 1200GS.
As for hopping between islands, I was going to say do a search of the forums, but the search on this site is pretty bad so... yeah it's possible to go Java, Kalimanatan, Borneo, Sulawesi and Flores by vehicle ferry. Don't know about the rest. You can always negotiate bike transport on Pelni, even big bikes. It's simply a matter of finding the right guy to pay off. To give you a rough idea of price, a Pelni guy in Makassar (Sulawesi) offered to take our 2 BMs to Balikpapan (Kalimantan) for about 1 1/2 times the cost of the ferry tickets. But we didn't haggle very hard, and didn't end up going that way in the end. But we're talking Indo rupiahs, not euros, so it's not going to break you.
You could easily spend 2-3 months in any of places you mentioned. And you probably already know this, but I can only say that the slower you go, the more time you spend in any one spot, the more likely you are to get to know the locals, and the more rewarding your travels will be. And yes you're right, for better or worse, Indo boat trips sure are memorable
Cheers
Lucas