Obviously many small landlords have a desire to accommodate their tenants problems although I have no understanding of why.

Vy, the tenant is seeking what's known as a reasonable accommodation.

If you're lucky the tenant will call you first the next time there is a problem and the tenant is not a "pro" who pulls this stunt every month;d) on the one year anniversary of the lease you get a written notice from the Housing office notifying you that there are too many people who need housing vouchers and the only way the City can accommodate all the needy renters is to drop what they are willing to pay you by 5%-7% the coming year.

If you sue her in small claims court, you'll have to travel there and get accommodations.  

What is a "reasonable accommodation" for purposes of the Act?

The only million dollar lawsuit I can think of that I learned of recently, was a woman in SF who successfully sued her landlord for discrimination based on her request for a reasonable accommodation, which the management continually denied for years.  

What other advice/strategies do you all have that will help us ease the transaction while accommodating all sides? 

I'm sorry, I can't accommodate you, but I understand that you might not want to continue living here.  

We have several student accommodations and the prime lease-up windows are late February - April (for those who are very organised and looking for a lease starting in May or September) and June - July (for those who are less organised, or were accepted in to a programme last minute).

And, we actually never had anyone want a reasonable accommodation to have a companion animal.