Ok, exciting update in locating a unicorn flyback. I think I found it.
Using Sears Parts Direct LOL
I started by searching all the model numbers Sams set 2181 covered -
CLB216P001, 2, 3
CLB226P001, 2
CLB227P001
CLB326PR01
CLB327PR01, 2, 3, 4
CL6682W
CL6685HN
CL6686P
CL6685HN was a hit on google! Linked me to Sears Parts Direct.
https://www.searspartsdirect.com/.../magnavox-cl6685hn...
This showed a Magnavox set... and I remembered GTE Sylvania Magnavox... all same sets under the NAP chassis....
Ok... looking at the parts, they listed a "Interface Transformer" Part #3618800005
Now let's google 3618800005
https://www.ebay.com/itm/294774995398
Woooo?! Sure looks like it. Just a black case vs white. Part number on the new flyback matches up to mine. 00361880-0005
Bought it last night. Fingers crossed. I appreciate everyone's help - not out of the woods yet. Not idea if the CRT itself is a goner. Hoping for the best.
This has been an excellent learning experience and I think I've found my new favorite pull your hair out hobby.