Is there a way to search in Contacts for a series of words and not get every instance of each word?

No, I'm afraid the search facility in Contacts is a blunt instrument and will return all the results it finds with your search terms - and this is also true for the iOS version.

You are asking for a search facility which can limit the search to a specific field - in your example a company name - or a phrase. Search in Contacts cannot do this. Some databases and software have a search facility where the user can limit the search to a subset of data or perform AND searching (rather than OR searching which looks at everything) but that requires a level of sophistication not offered in Contacts. Mitigating that, our collections are both small and very personal; because the contents are known to us they can be sifted easily.

Send some feedback to Apple suggesting some work be done. Contacts does not merit its own category on product feedback so send it via the MacBook option.

You might be interested in buying some contact software that offers a bit more power than the Apple Contacts. I know of two - but use neither - which seem to be popular and of course there are no doubt many others you could find in the App store.

Carhop by Flexibits and BusyContacts by Busy Apps offer a great deal more versatility than Contacts. The developer's also offer powerful calendar software which seems to me to be aimed at the office-level use and was more than I ever needed. They seem to offer purchase by single app, a bundle or subscription depending on the customer's need.

The software uses the Contacts database and syncs with iCloud so you can always go back to Contacts app.

With regards to searching, here on the BusyContacts webpage and here for Cardhop website are a description of 'smart filters' which are a sophisticated search tools.

If you examine them I'd be very interested to hear your comments.