Varying show-post number between views

Yes, you can do what you want.

The Loop In Action includes an example of a Different Archive Format. That, plus the Creating an Archive Index tutorial, should help you make the changes you need.

The Loop: Multiple Loops might help, too.

No matter how I format the archive.php, it looks like I will still be limited to showing 1 post per page no matter what template is being viewed. Is it necessary to employ a secondary loop? I’m not very experienced with PHP, so I’m not sure I’d be able to whip something up to make calls to the database and what have you.

Take a look at the following plugin:
https://rephrase.net/miscellany/05/perpage.phps
sounds like it might do what you need.

Here is another plugin to accomplish this:
https://mattread.com/archives/2005/03/custom-query-string-plugin/

Awesome! IanD’s solution worked. I’ll explore Matt’s solution if I need additonal functionality. Thanks for all your help, guys!