Nothing more than the Scale tool. I selected all the faces on one end, except for the final loop that takes you to the centreline. Then I squashed them slightly. Then I did exactly the opposite to the two loops either side of the centreline...stretched them.
Obviously, all you then have to do is to repeat step 1 at the other end. However, as I didn't note the scale factor when I squashed the first end...and to get it exactly the same at the other end, I actually cut the whole lozenge in half down the centreline, duplicated it (using Ctrl+Move) flipped the copy and joined the two halves back together again.
It sounds complicated, but actually took less time to do than describe.
It sounds like you're coming along just fine. I'm sure there will be hurdles...not least making sure the stl file is completely watertight, but you can rest assured that you can print just about anything in 3D from SketchUp...however curvy and organic.
It's a pretty lousy photo on my phone, but I actually managed to turn this
http://www.formfonts.com/files/1/11158/military-figures-various-positions_FF_Model_ID11158_4_usmil20_thumb.jpg
into this.
http://sketchucation.com/forums/download/file.php?id=41424&mode=view
I lost the fine detail on the end of the barrel...but this was quite a few years back
