Here is just one of a bunch of examples of what seems to me a pretty blatant disregard for the basics of property rights.

A landlord policy can be a commercial policy or a personal lines policy.It's the same as asking if you should buy a single family rental or a 1 unit building.Focus on the coverages and disregard the name of the policy.

I have come up with the same information as the OP - that an LLC owned by one person, or a married couple, is considered a disregarded entity by the IRS and there is no separation between the owner and the LLC.

Our LLC was solely owned by wife, and therefore a disregarded entity.  

I wold set up an LLC, as @Ned Carey stated you can elect to be treated as an S-corp for tax purposes or it can be treated as disregarded identity for tax purposes allowing you to report on your individual return.  

You might change it later if warranted.Reid - even though yours defaulted to the partnership, you will most likely be filing it as a disregarded entity / sole proprietorship anyway, i.e. no separate tax return.

I have advised the tenant to email the HOA so as to have some kind of record that shows they're not disregarding their rules.

Regarding depreciation, you claim it in the USA, when it becomes part of your NZ return it is disregarded or not allowed and effectively becomes taxable profit.  

While we are a forgiving community, the thing I see that most often results in people getting their accounts shut down is either blatant disregard of our no solicitation policy, or a disregard for the spirit of our community over the long haul.  

Your LLC files a schedule E as a disregarded entity unless you were to select to be treated as a corporation which is not suggested at all for your scenario.