The touring incarnation of “Shrek the Musical” that launches this summer in Chicago will be a somewhat re-tooled version of the show, including a newly conceived version of one character, a new song and a new co-director.Rob Ashford has officially signed on to co-direct the road production with Jason Moore, who helmed the Broadway incarnation. Ashford (“Promises, Promises”) has been involved in “Shrek” since he came aboard as an unbilled consultant during its 2008 out-of-town tryout in Seattle. Bill Damaschke, prexy of DreamWorks Theatrical, said the new, official billing reflected an ongoing relationship between Ashford, Moore and the production, and that sharing the helming duties will come in handy given the busy schedules of both Moore (on tap for next season’s “The Book of Mormon”) and Ashford (readying for “Leap of Faith” and “How to Succeed in Business Without Really Trying”). The three large turntables of the Broadway staging won’t be used on the road, so transitions and other staging elements will have to be reimagined. In addition, the dragon character has been reconceived with a new puppet, and composer Jeanine Tesori and David Lindsay-Abaire have written a new tune for Dragon and her eventual paramour, Donkey. Tour, which goes into rehearsal in Gotham next week, kicks off an eight-week run in Chicago July 13. Eric Petersen, Haven Burton and Alan Mingo, Jr. — as Shrek, Fiona and Donkey, respectively — lead the cast. With stops lined up including four weeks in Los Angeles and three weeks in St. Louis, the tour is booked through summer 2012, according to Damaschke.