Collecting and prepping parts aead of time is a great strategy. I spent a few years doing that, and it's awesome being able to just unwrap something that's ready to go when you need it (assuming you can find it!).
Another route for your frame would be to look for a "maker space" or something similar. Not sure where you are, but there are several in the Los Angeles area that offer workspace, classes, and even storage in some cases. Of course, you'll pay for it, but you may be able to plan your work in a way where you're paying for shop access for a week to make components, then hauling them back to your apartment until your ready for more. Another route is to look for a welding class that might also give you some shop access. Around here I've seen classes geared toward motorcycles, hot rods, bicycle frames, furniture, sculpture, etc..
Unless your going for full CAD for design and for cutting, you're going to end up doing a lot of hand fitting, especially of diagonals. Even with CNC cut pieces, you're going to be hand fitting some.
You could probably build many of the existing frame designs as sub-assemblies in about 3 sections, there's enough bracing in most cases so you could have rigid structures if you got creative. Clamp them together to work out overall dimensions and details, then, as others have said, mate the sub-assemblies when you have the space and equipment.
Yet another route, look for a garage, a yard, a shop or somewhere that will let you use/rent a corner or trade you for something. I have limited space and have built my frame completely outside with limited equipment. I keep it covered and spray can it as I go, and I'm planning to get it media blasted when complete and ready for final paint. In California I'm not to worried about rain.
I've got enough room to build and assemble in my back yard, but I'll have to take it apart to get it out.