Hi Carl - I would ExtractRenderMesh on all the parts - parts that should be joined (apart from the textured object) should be joined before extracting the meshes.
ExtractMeshPart the meshes to get at the relevant parts individually if needed but having the surfaces all joined up will ensure that the meshes join back again seamlessly.
Once that is done, I would do this:
- Isolate the textured mesh.
ExtractMeshFaces around each opening. The goal is to get just as few polygons from the textures dome mesh as is convenient as a separate mesh around each opening, then hide the rest of the textured object - it is massively dense, and bogs down the display etc. All of this will be joined up again later.
- Extract the mesh for each opening from the rest of the model the tubes etc.
- Isolate each pair (textured mesh stuff from around the opening and the mesh tube or whatever you want to stitch it up to on layers.
All of this is the make the operations more manageable - mesh operations on the huge dense mesh will be painful and eat up Undo memory very quickly.
Now, one pair at a time, proceed as Kyle suggests to bridge across - it may be worth pulling the tube mesh edges back just a little to make a clear separation all the way around .