I think Date::Manip is considered the slow (speedwise, not mental-capacity wise) cousin of DateTime. Either should be able to handle the fairly trivial case of timezone conversion. (What's not trivial is YOU remembering to use the same standard way of referring to time everywhere! Once you do that, adding some minutes is the easy part.)
I am also fairly certain that any mainstream module is going to rely upon the system time's GMT offset (e.g. -0500) rather than trying to disambiguate abbreviations, so no worries there.