Hello Peter Befuddled,
If your lathe is the same as the one in the photo there does not appear to be very much clearance between the forward/reverse shaft and the swarf tray. My lathe had the same problem which made it difficult to remove the swarf.
After putting up with the problem for years I mounted the lathe headstock on a block of 50mm thick high density polyetheylene (I think that's what it is called). The tailstock end is supported on two pieces of 1/2" UNF threaded rod. This setup made it simple to align the bed. After it was set up I made a tapered wedge block from two pieces of Tallow wood which fits under the tailstock end in the space between the two alignment rods. The two tapered pieces of wood are drawn together by two rods so that the block fits firmly to prevent any vibration. The system seems to work well.
Good luck with your setting up
Russell