This looks pretty good right now, but let's see what they say.

Currently, this follows the Sacred Heart (GR) style with Upcoming Events, myParish and Bulletins followed by their Facebook Feed.

In my humble opinion, I think this is a good fit for this template, then they can have a custom Archive for the Events CPT and a custom category display for News (including both pages and posts with the "news" category).

They have chosen to have only WP posts (to replace the FB posts), with a similar layout to Sacred Heart (GR). 
The title will remain "Parish News" but will display WP posts in a grid layout (2 rows of 4 posts) with Load More button below.

The math for that doesn't work out well to 8 posts at a time. I'm loading in 6 posts at a time (2 rows of 3 posts). Otherwise I can load in 12 posts at a time, if they want 4 posts in a row.

Unless I rewrite a completely custom retrieval method (or—at a minimum—write a super hacky workaround that would almost certainly lead to a bunch of errors), the AJAX Load More plugin adds pages as separate divs.

Thus, it would load 8 posts then 8 more posts for 16 posts. This would be fine when the viewport is big enough to display four posts in a row (or small enough to display two or one), but it would look terrible if the viewport is only big enough to display three posts in a row.

4-post rows
XXXX
XXXX

XXXX
XXXX

3-post rows
XXX
XXX
XX

XXX
XXX
XX

Below is a rough depiction of what it looks like when the math doesn't work out evenly versus when it does.

3 column is fine

This template looks pretty good, and is styled responsively too.