This is mostly a note to myself, but I thought I'd share it in case it helps somebody.
To get an Eagle PCB board outline & drills into Inventor, you use the DXF export utility in Eagle.
Next, click File/Export/DXF and save your file someplace. I stick them in a sub-folder of my Eagle project named "Export".
Selective Import, layers 20 and 44. Look at the drawing to confirm you're getting what you want.
Select "New Part - Project wires to 2D sketch"
Mapping options - Check "Map all layers ... single sketch"
Tada! There is your board as an Eagle sketch, properly sized, ready for extrusion.
Now, you might ask, "Why are you displaying those layers in Eagle for the export, but then ignoring them in Inventor?" The answer - it looks like Eagle has a bug. Without enabling all those layers, the drills don't come across. At all. Frustrating, but surmountable.
Also... if you're getting your boards made by OSHPark.com, then you can go ahead and extrude the board at 1.8mm in thickness. This is the same value for both 2 and 4 layer boards.