Can't search for linked contacts

I had a contact entry for a company, and another contact entry for an employee of the company (both contacts in the group linked with iCloud). The company contact had only the company name, but the employee contact had phone numbers, address, etc. So I linked the employee entry to the company contact (the first time I've used the link function). Now when I open the company contact, I see the phone numbers and address info,, and the linked employee in the LINKED CONTACTS at the bottom of the company entry. I can click on the linked employee name there, and it shows me the original employee contact card.. What I hadn't expected was that the original employee card was no longer visible in the Contacts list (I've since learned that's how it's supposed to work). Well, no problem, I figured, because I should be able to use the Contacts search function to look up the employee name, since it now appears in the company Unified Card under LINKED CONTACTS, and its card is still in the Contacts database. But no, for some reason, Contacts search doesn't find any sign of the employee name (and neither does iOS Spotlight Search). If those two search functions can find other details buried in a contact card (e.g,, the Notes field), you would think it should be able to find the names of Linked Contacts and at least show me the unified card. When the linked contacts feature was added, it looks like they forgot to update the local and global search functions. Any good solutions for this?