What it really comes down to is the availability of a 120/60R17 front tire in anything but a street product. Street sales wise a 120/60R17 is a VERY slow seller, and nobody is racing this size either so you're right about moving to a 120/70R17 and it makes the most sense. A 120/60R17 typically has a very triangular profile so I'd start by measuring your current tire diameter (or getting the specs) and comparing them to the 120/70R17 specs of your choice. Then move the forks a bit and go ride the thing. Depending on his pace and feeling for the bike you may want to raise the rear a bit, but at a track day lap time he may be perfectly happy.
Q4's aren't available in a 160/60 as of yet, the Q3+ is though. I would imagine its a capable enough tire, it was the spec tire for the Junior Cup series, and those kids are certainly going faster than advanced trackday pace