One small factor to consider: buying-down the interest rate on a loan means paying the interest up-front. That works-out well if you remain in the house a long, long time. The APR on the loan is most likely in the 6%+ range.
Not to minimize your pet situation, you’re probably scaring landlords buy tell him you have so many pets. Many tenants would say that they have one dog, then they move in the whole kennel after signing the contract. At that time, it’s a little late for the landlord to do anything about it. I’m not recommending that you do that.
I’m making these points to illustrate how the rental market generally works for the average renter/would-be buyer.