I can get 6" construction screws (#10) for $63.70 per 1000... the next available size is 7" (#14) @ $500 per 1000 ... OUCH!! Is it RECOMMENDED or REQUIRED to have 6 1/2" screws for attaching 4" EPS to exterior wall with 1/2" furring strips.

They need to be pancake head timber screws or they'll split the furring, and yes, they're expensive, which is another reason to go with standard lightweight siding and 1x (3/4" ) furring, so you can keep the spacing at 24" o.c. .

You probably don't need 1000 of them (or do you?).  You can get boxes of 250 for about $125-150 from web-stores.

FMHLGM712-250 HeadLOK (= spider drive pancake head, 7.5" timber screw)


 

It isn't widely understood that you want to cause friction and force transfer between the furring, the foam and studs - the goal isn't to hang the siding off of a protruding lever. So glue would help and stud penetration depth isn't that critical. Of course there may be specs that require otherwise.

I did this on my home addition with these screws through 4" of polyiso... it worked awesome. My only note is that I did have some 1x3s laying around that I was trying to use, and they didn't work (they split too often). 1x4s worked great though - definitely the way to go. I also used a corrugated plastic venting material (Cora-vent) to provide a rainscreen channel (I am very happy with the result). I hung fiber cement siding to finish off the envelope.