If your property is located in the City of Seattle, you have other options. Accessory Dwelling Units (ADU's) and Detached Accessory Dwelling Units (DADU's) are allowed in a single-family zone.
An ADU is typically built in the basement. A DADU is intended for the backyard. The city encourages these cost-effective methods of alternative housing. Check with the Department of Planning & Development "Client Assistance Memo" or CAM for more information about ADU's and DADU's. ( CAM 116A and 116B )
In most cases it is more likely that you won't get the re-zone and the plans are an expense that isn't warrented until you have the correct zoning.
Best of luck, sorry if it is not what you wantet to hear.
Also it is nice if you might have something to offer the city in return...improve the street, add sidewalks etc. What neighborhood are you in?