Not a Quilter and have yet to make my First stitch with my new ( to me) 306W BUT.... from what I have read, tension problems are very Common with 306/319 series machines that people have messed with in trying to get them to use standard needles. Something about raising the needle bar and then advancing the hook.... results in having to run very high tensions to make up for it. Since your machine had the other needles and i think you mentioned a needle bar adjustment..... I would look at your hook timing before I messed with the tension much. Just a thought i hope it helps . I am very interested in your progress as I have heard a LOT of negative about my newest addition ( 306W) and I am hoping that you ( and myself) will be the exception and be quite happy with our funky old Hybrid zig-zag machines. I got mine because my Singer 27 has no ZigZag and i want to be able to bar tack with a treadle.
Good luck and let us know how it goes. If you want and it will help I can link to a quote from an old singer techie on how to set up the hook timing and needle bar easily and without the gauges and such used in the service manual.