Apparently the issue has to deal with the fact that JPGraph won't let you overwrite its theme by default. I found by setting the theme to null allowed me to make more extensive changes. IMO, that's a pretty dumb setup, but c'est la vie. Here's what my graph definition looks like now:
$graph = new Graph( $p_graph_width, $p_graph_height );
$graph->SetScale('textlin');
$graph->graph_theme = null;
$graph->SetFrame(false);
The 'graph_theme' line is the new addition made that fixed the issue for me. I hope this helps others in the future as it's not explicitly stated in their API.