@welshweasel
You wanted robust evidence that helmets can correct cranial asymmetry. The following are quality peer reviewed papers, published in very reputable journals and are a good place to start:
Vles JS, Colla C, Weber JW, et al. Helmet versus nonhelmet treatment in nonsynostotic positional posterior plagiocephaly. J Craniofac Surg 2000;11:572Y574
Littlefield TR, Beals SP, Manwaring KH, et al. Treatment of craniofacial asymmetry with dynamic orthotic cranioplasty. J Craniofac Surg 1998;9:11Y17
Graham JM Jr, Gomez M, Halberg A, et al. Management of deformational plagiocephaly: repositioning versus orthotic therapy. J Pediatr 2005;146:258Y262
Teichgraeber JF, Ault JK, Baumgartner J, et al. Deformational posterior plagiocephaly: diagnosis and treatment. Cleft Palate
Craniofac J 2002;39:582Y586
Lee R, Teichgraeber J, Baumgarter J, et al. Long-term treatment effectiveness of molding helmet therapy in the correction of posterior deformational plagiocephaly: a five-year follow-up. Cleft Palate Craniofac J 2008;45:240Y245