Youth - my son is 7
Inexpensive - under $500
He has been using a LightSpeed QFR set and they seem to be working for him, but they seem to be a bit big on him.
I have a DC set with ANR. I think once you use an ANR set, you won't go back to a non-ANR.
I agree 100% with your comments about ANR.
I would not fly my kids until they would keep a headset on, probably 2 1/2 or so. At that time they also used a Lightspeed QFR. I think that they are one of the smallest "adult" headsets you can get. At first I had to tie up a rolled up pair of socks in the headband to get them to fit.
I had an old pair of DC (passives) but they definitely would not fit the kids, the headband was too stiff and could not get small enough for their heads.
Both my kids (now 6 and 7) have been using LightSpeed Sierras very comfortably for a while. It is possible that my kids have big heads but I think it is because even though the Sierras are bigger, they have a greater range of flexibility in the headband than the QFR's. My suggestion would be to borrow a set of the Sierras and see if your son likes them. If so, trade in the QFR for a Sierra ($600-$150 trade-in -->within your budget). The Sierra is actually really good, almost as good as the ZULU 2's that I use but plastic and not Magnesium.
At 7, this is a much easier than when they are younger, just put a headset on and JUST ASK HIM. I'm guessing that they won't fit but...has he tried your DC-ANR's?
Where are you located? If you are anywhere near me (Central Alberta), I can lend you one of ours and you can try it out.