Is it possible to merge entry parameters to create a dynamic field handle?
The Twig attribute function solved this for me. Thanks to @tom-bauer

Revised Template Code:

{% set newsSectionIds = craft.entries.section('news').ids() %}
{% set pressSectionIds = craft.entries.section('press').ids() %}
{% set entryIds = newsSectionIds|merge(pressSectionIds) %}
{% set entries = craft.entries.id(entryIds) %}

{% for entry in entries %}

    {% set sectionMatrix = attribute(entry, "entryMatrix"~entry.section) %}

    {% for block in sectionMatrix %}

        {# my matrix code #}

    {% endfor %}

{% endfor %}