Contacts on iPhone 6 will not merge with Cloud
The contacts can be cached on the phone hence why they show up if you search for them, although they are not going to be retrievable. The easiest way to get the contacts back will be importing the v-card files into iCloud.com/contacts under the settings, there is an import button.

Did you have the email account synced to any applications that are on a computer? For example in a mail application or outlook application, digging through them might allow you to pull the card files up. 

Another alternative is to go through the cache on the phone, and start typing them into the contacts application on a computer / iCloud, but thats a pain staking way to do things.

One theoretical way to get the contact files out of the unit would be to use a backup extractor, that can look at the database files of the cache, and pull the contacts out, you would have to do some searching to locate an application like this, although there should be some on the market (http://supercrazyawesome.com)