I don't know causing your problems, but you did talk about cheap film. Two issues come to my mind, include 'piping' and the second 'trapping' the frame.
If your film is cheap, it may pipe the light from the current frame into the next frame, in the cartridge, which would expose the front edge of the waiting frame, if you understand what I mean. Preventing piping is one of the qualities of 'good' film, but I don't how that is done, but it is a design and manufacturing isues that you pay for it with quality film. By the way, the cartridge could just be cheap through poor sealing for the film with poor 'felt', or synthetic 'lips'.
The second issue could be that the new film may simply be thin, and the pressure plate may not hold the film in the place where the film stops on the rails, and leak the light to the next frame i.e top right image causing the bottom left frame on the film frame? By the way, we're your exposures long, and were they compounding the film/gate/cartidge/seal issues?
Just some thoughts. Good luck,
Gary.
