Amelia,
The 1738 needle system sometimes know as a DBx1/ 287/16x1/or 287 are the same length as a standard household needle/ 15x1. The flat shank needles that came with your machines were probably 15x1s. The difference to you will be in the shank diameter. If the fat/ 2.02 mm shanked 15x1 fits your machine then any DBx1 will fit. If they don't fit then you will need the skinnier shank of the DBx1 which is usually 1.63 mm. I say probably because different manufacturers put them out in different diameters. Organ brand is usually a skinny one.
You said you had problems getting a proper stitch from a 1738. They have to be manually oriented, whereas a flat shank orients itself. Looks like your machine threads front to back. Correct? If so make sure that the long groove of the needle forward.
Talking to River and Fawkes nicely never hurts.
Hopefully that helps,
Cathy