Does the lease require you to fix the property? I would suggest talking to a lawyer near you. Use this site to find one familiar with landlord/tenant law. Good luck
As a general proposition, Tenants in Iowa do not acquire any possessory interest in the property they rent. They have the same rights if they have been in the rental unit for 1 year or 27 years -- None beyond the terms of the lease.
The only rights you have are contained in your lease. If it runs out in May, the new landlord has no obligations to extend it. If your self described "dificulties which are directly related" to "too much stuff" has reached the point where the new landlord considers the condition of your unit to be a nuisance or health hazard, she can terminate the lease on reasonable notice for cause. Just because she is insistent that you clean up the unit does not mean she is harassing you. May 31 is four months from now, and seems to be a reasonable time to give someone to clean up the unit, unless it has in fact reached the point of being a health hazard. I doubt that a magistrate in small claims court would concur with you that four months is an unreasonably "immediate plan".
The property belongs to the landlord and, subject to the terms of your lease and Iowa law, she has the right to determine how it is to be maintained.
The Iowa Civil Rights commission and the Iowa City Housing Authority have enforcement and investigative units for housing discrimination issues. If you believe you are entitled to special housing accommodations due to your disabilities, you should file a complaint with one of these agencies or consult with your case worker if you have one working with you.
Problem will be that unless someone with authority over your housing situation agrees with you and is able to permanently impose rules on the property owner that allow your current situation to continue, the ultimate result of refual to meet your landlord's expectations for care and maintenance of the unit will be your eviction from the premises at some point in the process.
You need to decide whether having a 28th year in your unit is more important than holding on to the stuff that the landlord objects to. If you choose to hold onto your stuff, and defy the new owner, you run the strong risk of losing both the stuff and the apartment.