I believe that was a similar problem another member in the forum had with his quad. Idled well and ran ok under low load but as soon as he tried to rev up it would cut out. You can get inline spark checkers that will tell you if you are losing ignition under load. Here's a link to one Home Depot carries. You can likely find one in a local auto supply or on Amazon. If the carb ran fine when replaced then the settings were likely fine. Plugged passages from sitting usually means a lean run problem. Hunter may very well have set the right course for you. . Not all apparent fuel problems are carb related, but like most that's the first thing I blame too.

Did it run OK after you had the carb replaced? The air screw usually is out about 1 1/2 turns +/- from lightly seated . If this has been happening since you got the new carb it may be the main fuel metering rod is set wrong .. There are notches in the top of it and a clip to change the amount it rises as you open the throttle. If the clip is in the lowest setting the carb will run the richest and in the top notch , the leanest. If this has been a problem right from the start with the new carb , try setting the metering rod one notch down from the top. That's where the rod is et on a friends Suzuki that uses the same carb..