Solved

For the benefit of those who may also have this dilemma, here's how I resolved this:
In my apache httpd-ssl.conf file:
1. I copied the existing Virtual Host block that I had created for mywebservername,com
2. In the new block I changed ServerName from mywebservername.com to niceURLgoeshere.com
3. In the new block I also set ProxPreserveHost Off
4. I restarted the Apache service, and I can now access my application using the niceURLgoeshere.com URL
I've kept the existing Virtual Host block in my httpd-ssl.conf file so that I have (for now) a 'backdoor' to the application.