Oh - you're CLIMBING in the tree... Wow! That IS adventurous. My hat is off to you for trying to get that to work.
Now I understand the problem you are having: Your slowest workable shutter speed is 1/125 sec based on your testing. You want a high aperture (f-stop) and if you put your ISO too high you get noise. I think that sums it up.
1. I would start by opening up my aperture a bit. I realize that a high f-stop is desired but I'm afraid we're going to have to make some compromises here. Set it to f8. That will double the amount of light entering your camera compared to f16.
2. I don't know how high your ISO can go. I'm guessing that on the camera you have that ISO 800 is already pushing it. So leave that alone.
3. In order to get a longer shutter speed (which you need in order to get a properly exposed image), we will have to work out a way to have that camera be steady without a tripod. Is there any chance that you can make/purchase some sort of rig that you can attach to the tree branches? Do you have a cable release so that you can fire the camera without touching the button? That way you could maybe hold it steady against a tree with one hand and fire it with the other.
4. Unlikely, but if you can get hold of a better camera that has a higher working ISO range, that would probably solve the problem. I'm talking about one of these new Canons or Nikons that has an ISO that will go up to the hundreds of thousands. With a camera like that, you could shoot with 1/125 shutter and f16 and get properly exposed images.
There is nothing wrong with what you are doing. There is nothing wrong with your camera either. But one of these 3 things: shutter speed, ISO or aperture has to change for you to get a proper exposure.
PS. I hate to dampen your enthusiasm but shooting a tree might not turn out as you are hoping. Trees have many fine, fine details and are subject to moving around in the wind and environment, etc. Furthermore, you are going to have to take a LOT of photos to get it to come out, especially if you are climbing around IN the tree, as you are.
In my personal experience, Photoscan does not like fine detail like hairs, branches, thread, etc. and it doesn't like moving objects, even moving a little bit.
So if this is the first thing that you are attempting to do in Photoscan, I would recommend starting with something simpler so that you can get a win at it.
If not, and you're determined to make this work, I hope the above suggestions are of some help.
Jon