Hi there
I would think that you have wear or slack on the carriage causing it to oscillate back and forth.
Have you adjusted the front gib strip?
If this does not work and you have a mill, you could lightly skim the edge nearest you and the middle edge. Make sure the carriage is set square on the mill before doing this
I believe most Myfords were run on the front of the bed.
I did this once a long while ago.
Can’t remember the reason other than a lot of wear was present and the lathe bed had been reground so was perfect.
I used a small cutter so I only took material of the front and back, not the top face that runs on top of the lathe bed. You might need to pack the front gib afterwards with a bit of shim at the front.
regards David