I have seen two or three types of speed controllers for vintage machines; the most common for me has been the carbon disk type, the other version has a type of resistance coil construciton. I think they can be serviced and adjusted. If you have the time and patience, you can give the "carbon pile" version a DIY clean up and service. There are tutorials on the web, perhaps you can find a repair guy who bothers to repair it. I have the carbon disk pile in both my knee controller machines, and in the Singer pedals. You have to post a picture of it to get more help or suggestions on how to go about it. I can let you know me knee lever 99 and Elna Supermatic are nice to use and have gradual speed control. Your Domestic should be just as good as any machine when sorted out properly.
The rubber wheel needs to be replaced, or maye you can sand it down to even out the bump. I think sewclassic carries these, and a few ebay sellers. These old machines are great, but they need to be cleaned and oiled now and then to run smoothly.