if it wont go in the machine... yes then you are correct that the timing is not the problem. if it fits in but the needle hits, or thread does not pickup then it could well be that some adjustment is not correct.
I have even heard tell that the later incorrect case was a singer replacement for the correct casse and was "the one to use" if you were going to retime for the 15 series needle. I have also heard told that it was a "factory approved and taught" procedure for the Scottish/UK dealers. I dont know and cant say... I do know that I used the one that came with mine, and followed the needle bar setting procedure the Hook end play and hook timing from the service manual ( and I checked the feed timing) and mine now sews correctly with reasonable thread ( no heavy upholstery stuff) at all width and length settings either straight stitch or with any of the first 10 numbered cams that I have. when I got it it was pretty prone to skipping one or more stitches per inch on any width setting above 2 (dial is maked 1-5).
SO..... I can provide some pictures and part numbers, but not for a couple weeks when Iam home, I can provide encouragement and advice if you wish to check all the settings, and I am still curious what does not work about a 319 case ( as I may need another some day )
Still really tickled that there is another 306 on the board and am looking forward to hearing of your adventures.