I don't know the design of your carrier, but if there is room in there, a thickness of tape or two will take the pressure off. I made my 5x7 carrier that way. I laid a negative on the glass and taped around the border with black photographic tape. I can't recall, but imagine it was two thicknesses. This made the negative very easy to position, and prevented newton rings even with my plain glass.

I don't know if your problem might be on the emulsion side; it seems like I had just one film type that had that issue.