A non-Views, Panels-compatible slideshow? The common way to create some variety of slideshow within Drupal is to use Views Slideshow and then display content that way. 

However, what if I just want a simple slideshow that appears in all of one Panel on the front page? Creating a new content type (and the requisite nodes) seems fairly overkill.

To that end — is there a slideshow that is both compatible with Panels and able to be invoked without using Views (or otherwise creating a bunch of nodes)?
umm sure. you can always make a Block using admin/structure/blocks with like full_html. You could then easily make whatever HTML markup you need to get your images on the page.

Then in your theme file include a scripts[] = /path/to/your/js-slideshow.js.

A slideshow is just a slideshow. For example the slideshow at www.ucsb.edu is simply some HTML for images, 1 custom JS file, and CSS to hide all but the first image initially -- this is easily reproducible with Core Drupal. You could then place the block wherever you want with Panels.

The only caveat with this approach is uploading images from Drupal to power the slideshow is obviously harder since your keeping it very lean and not 100% drupal integrated.

Edit

Another example of getting remote images into drupal could be seen here by Fago making Entities from Google Picasa images and slideshows. Unless your comfortable with all this custom code, I dont recommend this type of approach. Drupal may have many approaches to getting something done, but as I mention in my last comment dont fight drupal's conventions or default way of doing something simply learn to embrace it. I've seen this idea spread by MerlinofChaos telling themers (im paraphrasing) "learn to use Views css, even though its ugly -- its feature complete". The same applies to drupal 7 "table per field" default storage structure. When you try to work around what you perceive is a shortcoming you simply fight an uphill battle to make drupal do what you want.