I have a Solex I built out of a lot of different parts, including a lot of new/reproduction parts. It took me a couple of years to build it. I had help from a guy named Brian Colter, also known as Briansolex. He is the foremost Solex expert in the U.S. I have had a lot of pedal mopeds (like Puch, Tomos, Peugeot, Motobecane, etc.) and met him about 20 years ago on the Moped Army forum. He has a site where he sells a lot of Solex parts.
The front brakes are indeed a nightmare. I had to make a panic stop shortly after finishing the bike, and it turned the front caliper into a pretzel. It's a ridiculous design, but I haven't figured out how to install a proper bicycle brake on it yet. I just replaced the whole assembly, and am very careful with it. Using the decompression lever and dragging your feet on the ground will stop you faster.