I've used the Graphic -> PDF -> pstoedit -> DXF workflow a lot lately to create custom, intricate pad shapes for DipTrace and it works surprisingly well. Dimensions are maintained perfectly throughout the conversion process.
I really like this idea, because I can very accurately reproduce almost anything in Illustrator; the drawing tools are far superior to anything you'd find integrated into a PCB design program; drawing is Illustrator's specialty, and it's the de facto industry standard. This would be especially good for the silkscreen layer, because in Illustrator I can match text exactly, even if I don't have the correct font. Plus, I've been using Illustrator for about 12 years, so that alone makes things a lot easier.
Illustrator can export to .DXF, though there are sometimes issues with its .DXF files when used in AutoCAD. As long as they stay 2D they are fine, but I've seen some weird anomalies when extruding them to 3D. I had a trial program whose sole function was to convert .AI and .PDF files to .DWG and .DXF, and that did a beautiful job ("pdf2cad"), no issues even when extruding to 3D. It sounds like pstoedit may be just as good, and it's free. I see it uses ghostscript, which I've used in the past (along with GSView) for effectively turning my printer into a Postscript printer (which allows me to print halftone film positives for screen printing; you'd normally need a Postscript printer or [expensive] RIP software (such as Accurip) to do that.
Exactly! Since you've got Illustrator, you should be able to churn out pretty much anything you'd need vector wise.
One nice thing about pstoedit is it gives you fine grain control over the conversion. For instance, you can convert to two different types of dxf files: Plain DXF and DXF_S (which supports splines). You can also add switches that can convert splines to polys or even polys to lines, and you can do it with whatever precision you desire (which controls how many points it produces when turning a spline to a poly or a series of lines).
Now, that may not be important in Eagle, it might support DXF files with splines, I'm not sure; DipTrace doesn't, so it's very nice to be able to convert them to polys.
I use it under macOS, but it should work under Windows just fine if you've got Ghostscript. I love GS as well! I've got it setup in my Windows 7 VM to provide a virtual PDF printer. It's so handy to be able to "print" a schematic directly to a PDF.
My current project involves a cap touch panel with a large number of buttons; using GS I can "print" my board layout to a PDF and then import that into my vector editor, AutoDesk Graphic. Now I've got an exact copy of my board outline with the exact position of the buttons (that's fully editable since it's vector) which I can use to create the silkscreen markings and laser cutting pattern for the acrylic overlay that goes on top of the cap touch PCB! That saves me a ton of time that I'd otherwise spend recreating the board in Graphic.
Let me know if you need any help with pstoedit, it has a lot of options so it may seem daunting at first, but I've found it's actually pretty easy to use once you narrow down the options.
Edit: Oh, something else I've found handy lately, is when I'm creating a new part in my PCB software, I start by importing a manufacturer's assembly drawing PDF into Graphic, cleaning it up so only the drawing of the component remains (deleting the dimensions, arrows, etc.), scaling it and then converting it to a DXF file. I then import that to the assembly layer of the part I'm creating in DipTrace. Saves me a *ton* of time drawing the assembly by hand.
I've done this about a dozen times in the last week while looking for the right LCD for this project. It allows me to see exactly how it will fit on my board.