Hi! Sorry to Necro-Post, but I've been trying to figure out how to bake the texture from one UV map to another in modo, and I just nailed it this evening! So, here goes.
First, and most important thing to remember; when you add a new image in modo, it becomes associated with the UV Map that was selected at that time. You can't change it by doing anything in modo. You have to delete it and try again. So you *always* need to choose the UVs before you do anything else.
That being said, here goes!
The first question asked above was how to paint on all three body parts at once. The short answer is, you need to Remap the Avatar.
Fortunately, if all you want to do is paint on it, this is very simple, since it can be done automatically.
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== EASY AUTOMATIC REMAP OF COMPLETE AVATAR FOR PAINTING ==
• 1. Import the Avatar, or use one you've previously imported.
• 2. In List tab (middle right in 301 Default) go to UV Map, and choose (new) from the list. When the dialog pops up, name it.
• 3. Choose the UV Space display from the tab on the top. (Not necessary, but it does let you see what you're doing.)
• 4. From the Tool tab (top left) choose the UV Map tools (bottom of the right side tool tabs in that window.)
• 5. Click on UV Projection Tool (at the top.)
• 6. in the Create UV window that appears at the bottom, choose Atlas from the UV Type drop down. In the bottom part, where it has the stuff for the tool, make sure that Segment by Material is checked (you'll get larger pieces)
• 7. Click in the window that has your model in it. The UVs are made, and shown in the window that shows the UV Map.
That's it! If you just want to paint on the model, you don't have to do anything else.
(Except follow the directions for Painting on the Model, as explained in a previous post.)
You'll notice that you can paint on both arms and both feet; but bear in mind that only things that are painted on the RIGHT arm and foot will show up in SL.
Which brings us to the next bit. Obviously, things you have painted on that Atlas map aren't going to be any good to you in SL as they stand. They need the next step.
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== BAKING A REMAP TO THE LINDEN MAPS FOR USE IN SL ==
It's important to follow the steps below in EXACTLY this order. If you get them wrong, there's a good chance that your bake won't work, and you'll have to try again. (Also please note that when I was working on this, it failed to work for no known reason, and then modo crashed. When I restarted, all was fine. So, if you follow this exactly, and it doesn't work, try restarting modo.)
The maps need to be baked one at a time; so you'll have to do this three times (or twice if you're doing clothing, and don't need the head.)
• 1. Go to Statistics > Polygons > Material (lower right corner in the Default 301 layout) and click the + next to the Materials you aren't going to be baking. In other words, if you're baking the Upper Body, click next to Material_Lowerbody and material_head.
• 2. Tap the H key to Hide the selected parts, so they won't be on the baked texture.
• 3. In the Lists tab (middle right), click on the UV Maps flippy to open it, and then click the Linden map, whatever it's called. (If you're in the UV View you can see it, so you'll know it's the right one.)
• 4. In the Shader tree (upper right in Default) at the very top, you should see a drop down menu bar thing labeled Add Layer. Click on that, and choose Image Map from the menu.
• 5. In the window that opens when you do that, click on the thumbnail that has "new image" in the middle of it.
• 6. That opens a Save dialog. Browse to wherever you want to put the baked map, and name it. I choose targa format for saving, because it gives you a nice Alpha Channel that you can use to remove the black between the parts in the bake; but that's really up to you.
• 7. In the dialog that opens, choose the Resolution you want (I suggest 1024x1024, which is the default) and leave the rest at the defaults.
• 7. Your new image name should appear at the top of the Shader Tree, right under the white Base Shader ball. Right Click on the name, and it will open a drop down menu.
• 8. Choose "Bake from Object to Texture" at the bottom of the menu.
• 9. In the dialog that opens, leave the default of 0m, and click OK
• 10. Sit back, and watch it bake. You should see your image showing up on the familiar SL Avatar maps.
• 11. Close the Render window, and go to File > Save Image. The name and place are already taken care of.
• 12. Click U to Unhide the hidden parts, and Repeat the steps above for the other materials you want to bake.
And that's it! You're done. You can now open the images in Photoshop, remove the black, add your copyright, do any stuff you want to do in there, shrink, and save as a .tga file to upload into SL.
That's all there is to it!

/me does the Happy Dance!