The usual process is an initial application to amend the Zoning Code. This gets distributed through the city departments to see what effect the zoning change will have. Then with approval it goes on the to Planning Commission for public review. The exact steps vary a little from city to city but that is the typical process. Need to alert the neighbors and have a public meeting to listen to any concerns. Then final approval comes from the planning commission.
Let me know if you would like some help I am happy to do what I can. Talking to the city is probably the best option. You can get a feel for how they would feel about the change. If you are making a drastic change to the current zoning it will be tough to get it approved. What are the neighboring properties zoned as?
There is no clear cut rules that you will find in the municipal code if the zoning change will be approved or not, only the rezoning (or amendment) process (Title 17.20.020).