There appears to be a HUGE communication gap here or maybe I am misunderstanding. The link you provided

(www.jms2win.com/faq#sec-78)

to the tutorial appears to address the scenario when you are HOSTING your account with Godaddy.com. I have mentioned SEVERAL times that I

AM NOT

HOSTING MY ACCOUNT WITH GODADDY.COM.

Fassionate.com is registered with Godaddy.com ONLY. Fassionate.com is not hosted anywhere because it is supposed to be a slave site.

Knownogood.com is registered and hosted with Siteground.com.

Siteground.com uses CPANEL.

Knownogood.com is where Multisites is installed. Knownogood.com has Fassionate.com configured as a site.

How do I make it so Fassionate.com maps to knownogood.com/multisites/fassionate so that the user NEVER sees any links related to knownogood.com when browsing fassionate.com?

Is this software really this difficult to get working???

If Fassionate.com is registered in GoDaddy, you have there to specify that the DNS is Siteground.com.. (See video in tutorial step 0 - /tutorial that explain the concept and configure the DNS to redirect this domain to the appropriate hosting server - here Siteground.com)
In Siteground.com., you have to follow the hosting procedure relative to CPanel to setup Fassionate.com and share the same directory as explained in the FAQ CPanel /faq#sec-58.

In your case you have 3 elements to take in consideration.
- The DNS that must say that Fassionate.com is hosted on the server Siteground.com
- Siteground.com that must configure Fassionate.com to say that directory path is the one of your master website + ........./multisites/fassionate
- JMS that must be setup with the list of domain to recognize.

All you problem comes from the fact that you redirect the domain Fassionate.com that will by losing the URL and change it into www.knownogood.com.
As already told you, you can not redirect but really define a hosting.
Therefore, you have to setup the DNS to tells where is hosted the domain and not use a kind of webpage processed by your DNS to redirect to another URL.