How do I redirect a subdomain to a subdirectory in primary domain serving as reverse-proxy?

I'll describe the current setup first followed by what I'd like to change it to.

Current Setup

• Primary domain www.example.com pointing to a Ruby on Rails app deployed on Heroku.
• Wordpress blog blog.example.com running on Flywheel.
• RoR application serves as reverse-proxy to load Flywheel content under /blog subdirectory. For ex. www.example.com/blog/page1 loads content from blog.spacebox.com/page1. We're using https://github.com/waterlink/rack-reverse-proxy for making this work.

All of the above works as expected.

What We Want

Now the marketing team, wanting to up the SEO game, wants blog.example.com/* to redirect to www.example.com/blog/*

What I've Tried So Far (with failure, of course)

• Setup a Redirect on Flywheel dashboard to www.example.com/blog/$1 (expectedly resulted in infinite redirects).
• Deleted A record from DNSSimple for blog.example.com (pointing to Flywheel IP address), and replaced with a CNAME to point to www.example.com (didn't work).

With the above given stack, how can the desired result be achieved? What you recommend a stack change to achieve the outcome?

Much thanks in advance, as I've spent a good few days trying to make this work.