At NHA in 2009 the NAVAIR rep on the Flag Panel stated that in 2012 the Navy has to decide if the 60S can take over the AMCM mission or not. If no, then the Navy has to look into buy a replacement for the H-53 for that role. The 2012 date is based on the current 53E's reaching the end of their life in 2015. (I'm 90% positive he said that 2015 was the end of the life, but I'm 100% positive he said that 2012 was when a decision had to be made).
Those dates may have moved right over the last 1.5 years, but I don't think it will slide right enough to make a significant difference.
If the tow packages don't work for the 60S, then the aircraft can not do the job. So the MIW mission of the LCS has very little bearing on the engineering issues involved in the new AMCM capability.
If the 60S can't do it, then you either need to be new heavy lift helos that can do it or abandon the AMCM capability. If the engineers figure it out, then it's not an issue anymore and the 60S can do the mission.