Obtain a copy of the city zoning ordinances and look through them to see if you can find some wiggle room that the city inspectors didn’t notice. Typically these are set up as a matrix that have a long list of potential uses of land or building space, and then columns for “allowed,” “restricted,” “conditional,” “prohibited,” and possibly other categories.
You can find local government ordinances in the Minnesota State Law Library: Minnesota County and Municipal Ordinances Online:
If you can find some use that fits what you are doing and that would be something other than “prohibited,” you might be able to work with that. If the use is “conditional,” that means you would need to go through a conditional use permitting process. In that case, you should put together a document that describes how you would address various concerns that people are likely to have about agricultural enterprises that led them to prohibit them in the first place: noise, odor, water pollution, other nuisances. You would also need to address other things that are concerns for businesses: parking, traffic, employee accomodations, lighting, plumbing, bathroom facilities, structural soundness, security — all those details that might give an opponent an opportunity to argue that the business is not suitable in this space. The more proactive and complete you can be about that, the better off you will be in the hearing. You should also reach out to neighbors to gain their support for the business and see if you could get one or two to show up at the hearing to assure the city planners that they don’t object.
If the conditional use option doesn’t pan out, then you should request information from the City about their variance process and see whether it would be possible to request a variance. If so, then you should put together the same kind of document as for the Conditional Use Permit process — address every possible criticism, recruit the neighbors for support, and prove that you have a plan to be an asset to the community.
Contacting your city council member, and explaining your operation and asking for advice would be a pretty good idea, too.