back-formation

First, a back formation is the creation of a word, almost always be removing a prefix, suffix or any other alleged affixed component. Back formation does not apply to what you are talking about. Witch hunt (no hyphen) already exists, husband hunt also already exists (without a hyphen). I've never heard of "wife hunt", but i suspect that any native speaker of English would understand the intended meaning.

You've gotten carried away. You don't need to create an army of words with hyphens to get your meaning across--the first person who used husband hunt simply wrote it, and it was understood. English is not actually a rigidly structured language, so you can create any locution or even new words, and the test of the value of you neologism will be whether or not people understand what you intend.

Happiness hunt is nonsensical. I have no idea what you mean by "flat hunt," unless you mean to seek a residence--and although flat for a residence is not used in North America, i suspect it already exists. Americans will talk about apartment hunting. Job hunt already exists. You seem obsessed with hyphens.

They are dying out in British English: machine-gun, to-day, head-dress, motor-car, ear-wax, all now throughly archaic. Flat hunt is perfectly understandable and extremely commonplace in a BrE context. Giving the lie to the death of the hyphen, I found this in the showbiz news section of a London radio station's website:

"Cheryl Cole to flat-hunt with Bieber?

Justin Bieber has reportedly offered to go flat-hunting with Cheryl Cole in L.A"

(Cheryl Cole is an annoying talentless UK reality TV person.)

Well, the hyphen deserves to die. All of these locutions are perfectly understandable without the use of a hyphen. Fiona Batty-Plonk agrees with me.