Eagle isn't really free. KiCAD is free & opensource, and is really no less clunky than Eagle. KiCAD can output the files that OshPark will take, and last I heard OshPark was working on accepting KiCAD files directly.
Is manufacturing them yourself an absolute requirement? Or would you be alright with creating them and sending them to a fab to be made?
If you're alright with not making them yourself, you can use kicad which is a free CAD system for designing PCBs. And I would suggest hackvana as a manufacturer. He has very reasonable prices and takes care of things like panelization for you so you don't have to worry about it. You just give him your files, pay him, and he sends you the boards. He's also a super friendly guy.
Good luck! Sorry I couldn't help in terms of manufacturing them yourself, though it's much more involved and can be more expensive due to the extra equipment required.
I really like using KiCAD. It's free and cross-platform. Supports electrical rule checking, and auto routing. Will even print alignment marks if your are making two sided PCBs.
It has a bit of a steep learning curve, but this tutorial helped me a lot.
Mostly, but I would suggest either getting to grips with Fritzing - http://fritzing.org/home/, or better, KiCad - http://www.kicad-pcb.org/display/KICAD/KiCad+EDA+Software+Suite.
KiCad is really worth the time spent on that learning curve.
It should take you no more than an afternoon to get to grips with either and have board ready to be fabbed. http://dirtypcbs.com/ is where I would go to get them done.
You could always just spin a replacement board using KiCad and a PCB etching kit. Then desolder the IC's from the old PCB and resolder them on the new one.
You can then use this to cut the PCB you made to the right shape.
I'm doing a similar project. I breadboarded something that let me turn a blinky light on via web server/service. I'm doing mine in (free) KiCAD (there a subreddit for it too).
There a good YouTube series called Getting To Blinky that walks you through a basic PCB and how to send it to a manufacturer.
It's reasonably difficult, but probably not out of reach if you can get 8266s to work.
> Cadsoft Eagle
The only version of Eagle that'll support making a big enough PCB for a keyboard is the Professional edition. At $625, that's a pretty hefty hit.
Try KiCad instead.