Regarding a long vertical hotwire cut, your foam must be level/parallel to the ground in the lateral/widthwise dimension. If the foam is tilted slightly to either side the hotwire cut will not be perpendicular.
Haven’t tried yet (haven’t needed to). My approach to making a long perpendicular cut was going to be done with a my Rockwell Versacut mini circular saw (Dremel makes one too). Then that shallow cut serves as a handsaw guide, cutting slowly. Clean/true it up with a fence-post-level sander. If your foam surface is flat and no longer than 8’, you can use a length of square aluminum tube as a saw guide. Seems plausible anyway.
Greg Tate hotwire stringer cutting link;
And a Peaceful New Year…