Happy to find this space for 206/306 lovers! I have several 306Ks, one of them in daily use. It really is a great machine, once you overcome its eccentricies. I have found that DBx1 needles are a direct replacement for 206x13 needles. The length and eye placement are identical, the only difference being the 206x13 is flat shank, and the DBx1 is round shank. It's my opinion Singer simply ground a flat edge onto their industrial needles for these machines so they would "fit" into the universe of flat shanked needles on domestic machines. I use a tweezer to orient the needle by the scarfs, then insert it into the holder. Works like a charm, plus, you have a FULL range of needles available. I have used both Organ and Groz-Beckert DBx1s without issue.
Received my newest, a black 306K, the other day. Am busy cleaning and waxing, she's a beauty and will shine like brand new when I'm finished.