Megabeasts and titans only appear if you have a minimum of 100000 bucks and 80 population. Forgotten beasts can attack much earlier, but they cannot be captured. Usually a lot of the megabeasts die before the end of worldgen, so you could try ending worldgen earlier (maybe after just 50 years or something). I guess your setting might make it more likely for megabeasts to appear, but they don't come very often for me. You might have to wait for a few years.
In addition I set the cancelation on megabeast-deaths to 25% at one year before generation stoppage, so there were at least 75 present on the map when I embarked. It payed off. Roughly half an hour after I posted my qestion, a female dragon appeared. Not even half an hour after that, a male did. But I guess from your answer, that there's no way to aktively encourage them. Not even with a very high worth of your base?
The trainer usually reinforces training before it reaches semi wild, sometimes even if it's already well-trained. If your trainer is good enough it would take a long time for it to reach semi-wild. If you want to level up your animal trainer, just breed a lot of dogs and get him to train all of them to war dogs. So don't worry your dragon won't kill everyone.
I've got about 30 dogs and a lot of captured underground animals. So training the trainer is, and was, well on it's way (even had to butcher a lot of war dogs, because they started to attack each other^^).
However, you have to make sure that the dragon does not kill any of your dwarves before it's tamed. If it does, then it may go around eating stuff even after it's tamed. I'm not sure if this bug has been resolved, but it's been around for a while.
I think that should be fairly easy to achieve with a remote pasture/training area. My base defences are (possibly apart from gaseos Beasts) practically inpenetrable (if i don't forget to pause and wander off), so the possibility of them engaging in combat are next to zero. The only trouble would be if they reverted to a wild state, which is the reason why i trained them within their cages until now.
If there are only blood thorns in layer 3, that means there's no water in layer 3, so no tunnel tubes or any other kind of tree. Tunnel tubes can also grow in layer 2, so go check layer 2. If they're not there in layer 2, then unfortunately there's no way you can get tunnel tube logs.
My mistake... what I meant to say was, that my map contains blood thorns which only grow on layer 3. My map has only 2 layers of caves. The meager space on 3-layer cavern maps was really annoying me. There was water, even infinite sources on the edge at one point, but i drained it into open space for more growing area. And everything grows... except Tunnel tubes... which did grow on another map with the same cave configuration.
While this might be the wrong section for this question: Is there no cheat... ups... I mean mod which could achieve this? (btw... if you don't know of one, then don't start searching, I'm in the process of doing it myself already.)