NEW YORK - Stagehands and producers negotiated until nearly midnight Friday, hoping to resolve contract issues that could shut down much of Broadway just as the fall theater season gets under way. Both sides agreed to talk again Tuesday, said union spokesman Bruce Cohen. Discussions reportedly had been tense this week between Local One, the stagehands union, and the League of American Theatres and Producers. Most of the conflict has involved the thorny issue of load-ins, the complicated physical setting-up of a show in a theater. Producers say the rules governing load-ins are cumbersome and expensive, requiring more stagehands than needed. The union says the rules are necessary. The League initially set a Sept. 30 deadline to resolve the conflict and threatened to lock out the stagehands if an agreement was not reached, but talks have continued. The union, a member of the International Alliance of Theatrical Stage Employees, has been working without a contract since the end of July.