How big is the sweet spot for the vandersteen quatro wood CT speakers?

I would just call Richard, he answers the phone

read the manual and try to follow the extensive setup advice before you call

Also buy a small level laser it will help you with aiming
your 13’ dimension seems to infer you have them stuffed in the short wall corners..... see if you can relax that a bit....

If you've put the Quattro's deep into the short side corners (along the 13 foot dimension), try moving them out of those corners, a few feet from sides and at least a foot from the back wall. "Sweet spot" is fairly wide, laterally, with Vandersteens, but in my experience sound is a lot more focused when you're sitting down (not standing) in the "zone." The Vandersteen rear-firing tweeter (if turned on) helps ameliorate this problem somewhat. Good luck, and don't be afraid to experiment with speaker and listener position.  

I own a pair of Quatro Ct's myself.  Very enjoyable speakers!
Will your dealer be doing the setup?  If so they should have the tools necessary to dial in the speaker.  I think the sweet spot of the Quatro is less sensitive to lateral positioning than it is to vertical.  Also, don't be too prescriptive in the placement of the speakers and/or listening chairs.  The optimal listening position (sweetspot) is usually a function of all of the conditions that you seem to have pre-determined.  Be flexible...

Thanks for all your input and suggestions. John at audio connection in Verona New Jersey will be doing the install. From what I've read on the internet there shouldn't be any problem, he's very qualified