Can I exclude a commerce address by ID when retrieving a list of addresses?
I still haven't found a succinct way to exclude a particular address by ID within the commerce customer addresses tags, but I did come up with the following as a way to get a nice clean set of addresses I want to iterate over.

Rather than use a conditional in my loop, I decided to create the collection first, with the address I want to exclude being kept out of the collection. This gets the job done!

{% set customerAddresses = [] %}

{% for address in craft.commerce.customer.addresses %}
    {% if address.id != craft.lhngroups.orgCommerceAddressId %}
        {% set customerAddresses = customerAddresses|merge([address]) %}
    {% endif %}
{% endfor %}