No one wants to be in gymnasium in May and April when the weather starts to turn nice. I always enjoyed getting outside for spring sports. Maybe one gimmick you could do weather permitting is bring mats to the football field and have an outside match.
I think you would lose participation significantly moving to spring. Competing against baseball, track, tennis, Lacrosse wouldn't be good. There's a good reason the upper Midwest is so good at wrestling and the south sucks at wrestling. The reason is the weather. Its cold in the winter in PA, IA,MN, NJ, OH, MI, IN, NY, WI, NE,MO: so the next best thing to do is go to a gym and wrestle. I think that's the common denominator. In the south and west, weather isn't so bad so kids are outside doing stuff, but not wrestling.
Also, a lot of wrestling referees also officiate baseball and softball. I think you would have a tougher time finding refs.