This is mostly really good; the only problem is the address section, as you said. The issue with the <time> element is that it is an inline element by default, so therefore doesn’t span across the full width of the page. Since it is sat on the left hand side of the page, the class won’t make it align to the right. This can be fixed by wrapping it in a block level element like a <p>, and putting the class on there instead.
In addition, <address> is a block-level element, so it doesn’t need a <p> wrapped around it. and you don’t need so many <br> elements — <p> elements create their own line breaks by default.
I made the fixes described above in the following code snippet:
<address class="sender-column">
<strong>Dr. Eleanor Gaye </strong><br>
Awesome Science faculty<br>
University of Awesome<br>
Bobtown, CA 99999,<br>
USA<br>
<strong>Tel:</strong> 123-456-7890<br>
<strong>Email:</strong> no_reply@example.com
</address>
<p class="sender-column"><time datetime="2016-01-20" > 20 January 2016 </time></p>
<address>
<strong> Miss Eileen Dover </strong><br>
4321 Cliff Top Edge<br>
Dover, CT9 XXX<br>
UK
</address>