Apologies for the confusion, NG+ is fully intended to be played on free play. I have changed the rules from being vague about the mode to be played on to specifically state that the category is reserved for free play, on both Co-op and single player.
@zulice Both LSWI and LSW:TCS have the same vague rulesets that do not distinguish which mode is to be played on. As you can see on the NG+ single player page on LSW:TCS (http://www.speedrun.com/lswtcs#Any_NG%2B1) I have a run submitted (albeit I cannot view it at the moment, technical difficulties) that I am very sure used free play mode throughout the entire run. However, you are correct that almost all other runs have used story mode. I'll delete my record to help avoid future confusion.
LSW2 runners will have until May 18th at midnight EST to vote on implementing the PC load remover.