I'm not so sure that your reaction will work that well. I was under the impression that grignards generally don't do SN2 on alkyl halides very well... if they did you would never be able to form the gringard in the first place (since it would just homocouple with any unreacted alkyl halide). I think you may have to consider adding Ni (first two ref's) and/or switching to Zn instead of Mg (last ref):
Terao, J.; Ikumi, A.; Kuniyasu, H.; Kambe, N. J. Am. Chem. Soc. 2003, 125, 5646-5647.
Terao, J.; Watanabe, H.; Kuniyasu, H.; Kambe, N. J. Am. Chem. Soc. 2002, 124, 4222-4223.
Arp, F. O.; Fu, G. C. J. Am. Chem. Soc. 2005, 127, 10482-10483.