Definitely check into a variance. For most subdivisions, they come with deed restrictions that govern your structure placement on the property ... and also for most subdivisions, they fail to renew the deed restrictions. If you're in an area that is fully occupied and land-sales and developers have moved on, there's a good chance the deed restrictions have expired. Usually a check with the county engineer can confirm if active deed restrictions are in place, or if they have expired.
And yes, be courteous to your neighbors. It might be good to have them write out acceptance of your proposal before you apply for a variance. Municipal offices are often very understanding depending on the proposed use and how old the property is. My house was built in 1925 - when very few people drove cars. The house on my right still has the original carriage house. The house on my left was allowed to add a 2-car garage all the way up to the property line - provided that he gutter the roof and direct any watershed back onto his property.
