One illustrative method disclosed herein involves forming an integrated circuit product comprised of first and second N-type transistors formed in and above first and second active regions, respectively. The method generally involves performing a common threshold voltage adjusting ion implantation process on the first and second active regions, forming the first and second transistors, performing an amorphization ion implantation process to selectively form regions of amorphous material in the first active region but not in the second active region, after performing the amorphization ion implantation process, forming a capping material layer above the first and second transistors and performing a re-crystallization anneal process to convert at least portions of the regions of amorphous material to a crystalline material. In some cases, the capping material layer may be formed of a material having a Young's modulus of at least 180 GPa.