Chris, I don't think he was looking for a lecture from you. Heart attacks, really? lol...
Maybe they should ban dogs and cats and Harley Davidsons, as I'm sure many people are deathly afraid of them as well. He has already admitted he made a mistake, and said he would not do it again.
I think your landlord would have a hard time kicking you out, considering he knew of your animals prior to signing the lease. You may want to check your copy of the lease to see if there is a pet policy anyway.
You have done the right things, appologizing to your neighbor. If your landlord
continues to push forward with eviction plans, you can offer him a pet security deposit of a few hundred dollars. I don't think you should have to do this, as he already had you move in and sign a lease already. You may want to see if you can discuss this with a lawyer so you know your rights. Good luck!