Hi Keith,
My wife and I just had our little girl at CIMA. We were incredibly impressed with the service and care. We stayed away from Catolica at our doctors strong suggestion. His comments where that Catolica is terribly about communications with the doctor and often times that slows things down because they do not allow the doctor full access to what he might need.
As for the rentals, we too had an issue as we live in Guanacaste, but needed a short term rental in Escazu to be near the hospital. We also have a large dog and two cats. While it isnt the most honest thing to do, I suggest you not mention you only need two months. Go ahead and sign a full lease and then leave after two months. It is perfectly legal and within the limits of the law. The laws here heavily favor the tenant. The downside? You will loose you deposit so make sure you negotiate it as low as possible.
You might want to do some more research regarding Catolica. If you decided CIMA is a better option, there are some GREAT neighborhoods within 5 minutes of the hospital where I imagine you could easily find a rental.