We have been using single .fbx files exported from MAX that have several meshes in them. Naturally, we have the same problem where all of the meshes that were exported into the same fbx show up at the origin with an unexpected orientation and scale (if we scaled them inside of MAX).
We overcome this problem as such:
1.) Build your scene inside of MAX as normal. Do all your moving and scaling and rotating as you have already done.
2.) Individually convert everything to an editable mesh if you haven't done so already.
3.) Select the box in the center and then go to the Modify tab. Click the 'Attach List' button and select the other meshes that will be part of the export (the two cylinders in your case).
4.) At this point, you have sort-of one big mesh. Depending on how you use it, this may or may not be enough for you. Most of the time you will want to break it back apart into the individual components. If so, proceed to step 5.
5.) Select the Editable Mesh, expand it under the Modify tab and select "Element". This will let you select the individual pieces that you attached. Select each element then click the "Detach" button and give it a name. Repeat as necessary for each element you originally attached.
Once you are done, each mesh will be properly oriented in your exported FBX.
Granted, this is far from ideal in that it is a tedious process and is almost unusable if you have a large number of individual elements, but it has served us well over the last project. We tried moving the pivot points manually and could not seem to get it right. Then again, I'm no 3ds MAX expert :-(
Good Luck!
-Jeff