You might try Etsy.com. It is dedicated to offering primarily hand-made and small-business items.
I found that once I thought out the process and tackled making a neck it wasn't that difficult... but it is precise and time-consuming, and it has to be perfectly flat. That means starting with a perfectly straight piece of wood, using a level or metal straight-plank to glue the fingerboard to the neck, letting it set a full 24 hours.
Curving the back is a surprisingly simple process once one gets it down. Use of a draw knife (old way) or router (new way), and then finishing with sandpaper in "shoe shine buffer) fashion works great. You can also use an oscillating sander with rough sandpaper to form out your neck and then change pads for varying degrees of finish.
I'm sure there are pre-made necks out there and there's surely nothing wrong with using one. But the adventure and reward of "made it myself" makes it worth the journey. Just be sure to get it all planned out on paper and measured ahead of time. : )
Ah space problem. I hear that. Here's a solution I've tried in the past that works well. All you need is a bench vice and room to use it.
Clamp the wood so it stays put. It is amazing what a shark-tooth rasp can do in removing wood very quickly. In 30 minutes or less of some elbow work you can totally form out a neck with a simple quality rasp. That includes the rounded back, headstock, and any pickup space you need to account for. Then you use a regular file to remove the rasp marks, and sandpaper to remove the file marks. The result is a fully formed neck in 30 minutes to an hour-- definitely a reasonable time for such a project.
Then drill, oil / spray / whatever, let dry, and install. The room needed for this process is minimal and it produces good results at the lowest possible cost. Bench vice, rasp, standard file, sandpaper. Couldn't be simpler. : )
Now, if you add frets that brings in a bit more. Fret methods are numerous and a whole different ballgame. But it requires no more space: just a simple bench vice and the proper fretting tools.