After realizing that the {count} value isn’t cumulative, and it starts counting anew with each page, I decided that Lisa’s suggestion was perfectly reasonable considering I was limiting each page to twenty entries. Here’s what it looks like, and it works like a charm.
{exp:weblog:entries orderby="date" sort="desc" limit="20" weblog="{master_weblog_name}" cache="yes" refresh="60" disable="categories|custom_fields|member_data|trackbacks"}
<td>{count} {title}</td>
{if count == "4"}</tr><tr>{/if}
{if count == "8"}</tr><tr>{/if}
{if count == "12"}</tr><tr>{/if}
{if count == "16"}</tr><tr>{/if}
{/exp:weblog:entries}
Although I would’ve liked to condense the count condition to something like this {if count == “4|8|12|16”}{/if}, but that didn’t fly. That’s just me nit-picking. 
If the count value was a cumulative representation of all of the entries, I would’ve needed to perform that modulus operation via PHP as described above by Robin.
Thanks for your help, Jill and Robin. I owe you beers.