Wire wrap and approaches like that are long gone. The only decent way is to have custom boards made. There are some places that do this fairly inexpensively. For simple stuff you can do your own, but for the boards I do now, it's cheaper to send them out.
The fun part is soldering. I have a hot air station, microscope and some other tools which allow me to hand solder many SMD parts, but there are some that are very difficult to do that way. The main Bottlehead board is a board that is almost impossible to solder by hand, so the only way to do it is have a professional assembly shop do it. There are lots of these around, but none of them are cheap. There are some that specialize in prototype work and I use one of those. So I send off board files, XY files and BOM files, Doc sends them a big chunk of money and a few weeks later we get finished boards.
I then test them out, find problems, and hack the boards up, cutting traces, adding tiny little wires etc, all dome under the microscope. I get it working, then go through the process again to hack up one for Doc and send it to him. Thus all the boards he has had so far have a certain amount of red wires and cut traces.
The ones in the fab right now have all the hacks from the last version incorporated into the board and hopefully will work out of the box.
John S.