After years of delays, the city presented a new plan Tuesday to move forward with repairing the sinking backyards at Villa Maria Homes — and this time, not every homeowner has to sign on before work can begin. Built in 1990 as part of the city’s post-arson rebuilding of the South Bronx, Villa Maria Homes is a 114-home affordable development in Longwood. Behind its tree-lined streets and neatly maintained homes, residents have spent decades grappling with infrastructure problems the city says stem from poor initial construction. Previously, city officials said they needed consent from all 114 homeowners because the underground drainage system connects clusters of homes. Under the new approach, officials will instead begin construction on a 13-home cluster where every homeowner has already signed.