If it was a chain stitch full size, it's very likely it was a Standard. I believe the only Singer chain stitch for domestic use is the small model 24. I've read that there was a chain stitch adapter for the WW, and also one for White Rotarys, but they are quite rare.
The plate for the chain stitch has a notch at the back to let the thread not get pulled by the plate as the feeds move the fabric. It could be what is giving you uneven stitches - as the thread rubs on the plate as the loop is being tightened by the next stitch.
I may have an extra one. In my search to completes full sets of attachments, I've often ended up buying 2 - 3 partial sets, and often they also came with the chain stitch plates. I'm going to be so happy when I finally get my attachment sets organized, so I can have a separate location to put all the extras that I can pass on to others.
I'll see about getting you a copy of the manual too. I've tried to collect an appropriate manual for each machine in my collection - and some day I'll have them all scanned so it will be easy to share.