Weaving poly strings, even stiff ones isn't that bad if you do it right. Stringing one ahead is a good start. Also, if you weave the crosses by pushing the tip of the string through, you might try pushing a loop through instead. You make a loop that you push/pull through the weave instead of weaving the end of the string. You do this because of the wire-like nature of poly, the bend memory, gets in the way of the first technique where the loop push/pull works easily. In addition, if you weave straight across the racquet, try incorporating the vertical space available when weaving. That is weave at a diagonal to give yourself more space to work with.