I agree about the 10 day trip - or anything longer than a week you can find and manage. Crunch the flights, eliminate possibilities, eventually your head will stop spinning and you'll get a handle on it. You might be able to squeeze the longer itinerary in 2 weeks-ish, though that doesn't leave any margin for error and any length of stay in Hong Kong will make it harder. You should definitely pad things on the arrival end, both to rest and to reduce chances of missing the boat! On the return you could schedule it tighter if you can deal with a delay if something doesn't go quite your way. Perhaps time in Hong Kong on the way can double as rest time if the flights work, or as buffer on the end that you could skip if you are delayed?
After Garuda, which most seem to agree is the most reliable and also has the dive gear allowance, I see a wide range of opinions on other Indonesian carriers. In the second tier, everyone seems to have some they swear by, and some they swear at - some probably based on which airlines screwed them over and which ones they were lucky with, and varies some from person to person. We used Garuda, but I heard a lot of positive things about Batik from the crew. I'd avoid the bottom of the barrel.
We recently did a repositioning trip and it was great to see several different areas since it was our first time there, though we didn't really see enough of any area. I also liked Misool best. We didn't experience any dynamite fished areas on our trip, though they said it does happen that a site that was good the previous trip is toast the next. Maybe we were lucky, or maybe they had good enough intel to not put us on any sites like that. There were a few dives during the transit that weren't quite as good, pretty much a decent place they knew of along the route so we could get in a couple dives before continuing on. Also on the downside were the days with fewer dives and the long crossings (though I kind of like being forced to do nothing but relax, and I don't get seasick so that helps.) All irrelevant to the OP right now since they don't have the time and those trips are booked even further ahead, since there are few of them.