It has been 4 months since I posted on this, and I think I am in a place where my yard flooding issue is tied up. It certainly did not make for the best first rental experience, but I am persevering and just now getting back into a mindset where I would like to try another property. For those that are interested, here is how my situation turned out.
From some of the suggestions posted above, I began to look at what my options were to best address the flooding issue. I wanted to balance cost with a fix that would actually address the problem, and I wasn't convinced that just bringing up the grade would solve my problems. In fact, I was concerned that this may actually result in other problems with neighbors getting water on their property. Well, I obviously didn't act fast enough because my property management company's broker received a ticket from the city along with a request to appear in court. This is a whole different headache I had to deal with that I won't get into here, but it is looking like they are charging me all the legal fees because I followed their guidance to keep looking for a solution, when in reality we were already in violation of the city's requirements. Anyways, I digress.
With the pending ticket issue, I stepped up and took the lead instead of letting my property management company look for a solution. Maybe I should have done this earlier to save me the anxious, but I quickly found that by getting involved stuff got done much quicker. I started with a "survey" of the property that my father and father-in-law completed to get an idea of where our low spots were. I also talked to a lot of people including the city engineer, an engineering firm, two plumbing companies, some landscapers, and an attorney. A few options I entertained to address the flooding included yard grading, a drain tile that could be run from the backyard across a neighbors property to tie into a city drain, and a culvert in the back yard that could be tied into my property's combined sewer system. While I was leaning toward the drain solution, this became pretty involved and did not create a very quick or cheap fix.
My final decision was to go back to the very first idea and start with some grading. The rational I used to make this decision was 1) I would most likely need to do some grading with any of the other options I was looking at, 2) it was the most cost effective option, 3) I found someone that was relatively confident they could do the work with the intended result by contouring the yard in a way that would direct water back to the driveway and out to the street and not onto neighbor's yards, and 4) the city stated this was all they would need to mark that finding as complete in their files and issue my landlord license.
So how did it work? Well, I have obviously not been through a spring thaw yet, but there have been some big rains in the last few weeks and there has been no water accumulation in my yard or neighbors yard. So time will tell, but I am hoping this issue is put to bed.