Managed to solve the issue.
I have a main Rails app running on Heroku at https://www.mysite.com
I installed WordPress on Heroku and have it running on a different url.
I have a reverse-proxy set up on my Rails app, such that my blog looks like it is running as a subfolder: https://www.mysite.com/BLOG_AS_SUBFOLDER
Here is my .htaccess
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /BLOG_AS_SUBFOLDER/
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>
<IfModule mod_headers.c>
<FilesMatch "\.(svg|ttf|otf|eot|woff|woff2)$">
Header set Access-Control-Allow-Origin "*"
</FilesMatch>
</IfModule>
The only thing I had to change compared to every other answer on the internet was to modify the following line:
RewriteRule . BLOG_AS_SUBFOLDER/index.php [L]
to
RewriteRule . /index.php [L]
Rhyun’s solution will not work once heroku restarts (which is whenever you deploy, or randomly once a day, if you use it as a free service)