Hi Greg,
so because text on a path is not working, you have two options:
[1] Do every character in its own frame.
[ 2.1 ] Do rotated text by using the Japanese paragraph composer.
[ 2.2 ] Then rotate the text frame.
I assume that you are not using the Japanese version of InDesign so the Japanese paragraph composer is not directly available through the GUI. But you can apply it to selected text by scripting.
Just did it here to the special character auto page number:
https://community.adobe.com/t5/indesign/make-page-numbers-appear-in-column/m-p/11168048#M188186
The code is below.
Just select all the text you want to rotate by 90° and run the following ExtendScript code on your selection:
// Text selected.
app.selection[0].properties =
{
characterRotation : 90 ,
composer : "$ID/HL Single J"
};
After I selected all the text in the frame and running the script the result is this:
( Note: Also set tracking to value -100 )

The result can be published online without a flaw:
https://indd.adobe.com/view/c61fe0a3-5981-4ff8-911f-78ca7c4a4a42
By applying baseline shift you could fine-tune the position of single characters like the starting "C" of "CLASS":
( Original position in gray. Did baseline shift with -3 Pt on the 72 Pt "C". )

How to work with ExtendScript code, save a script file, install and use it, see Marc Autret:
http://www.indiscripts.com/pages/help#hd0sb2
Regards,
Uwe Laubender
( ACP )