Yes that might help. In "the old days", film and/or backing paper were thicker than now. So the roll would be thicker and hence move film a bit further. If the spacing is too tight on your camera, there is an easy trick to compensate to a certain degree: When you open a new roll, it's held together by a paper strip around the roll. Open it cautiously and leave a part of this strip attached to the backing paper. Insert the paper strip into the take-up spool and wind. The beginnig of the backing paper will follow. Wind, until it's firmly engaged. Your spool core is now a little bit thicker than usual. This might solve your problem, just have a try.