The producers of “To Eliminate a Mockingbird,” a hit perform that experienced been packing in audiences before the pandemic, introduced Wednesday that they would shut down the demonstrate right up until June, lay off the solid and crew, downsize the output and then reopen in a more compact theater. At the exact same time, “Woman From the North Nation,” a coronary heart-tugging musical that employs the tracks of Bob Dylan to look at the Melancholy-period plight of a group of down-on-their-luck Midwesterners in the town wherever Dylan was born, explained it would close its Broadway operate on Jan. 23, and would test to reopen in a further theater this spring.…