Hi Everyone - Here is the solution.  It took an architect in my company to know how to go after this custom field:

https://mycompany.service-now.com/api/now/table/sc_req_item?sysparm_query=number%3DRITM2365756&sysparm_display_value=true&sysparm_fields=variables.my_custom_field

The "&sysparm_fields=variables.my_custom_field" was apparently the key.  

Thank you very much to everyone who helped.