Its interesting they would upcharge you. I wondered what would happen if one did submit at the economy rate that were a little over PCGS's $300 Price Guide.
If it's like 305 or 350 generally they wouldn't but NGC was usually the bigger stickler for it. That could have changed though. The 300 declared value might be a bit of a red flag to double check it given that's the limit too. Who knows though maybe there was a big string of people trying to slip things by so they cracked down on it
Actually, they pay their determination of the value (which often turns out to be less than the price guide) or the value on the submission form - whichever is less.
Their own imagination? It's proprietary and isn't disclosed. You get a check, take it, or leave it. I -imagine- they do things like check auction records, but whatever information they use doesn't seem to make the circle back to the price guide. There is, of course, an incentive for the price guide values to always be increasing and not to decrease them even if the market says otherwise.
The first thing they'll look at is what your declared value was. Whatever number you put there is the maximum you can get no matter what so if you submitted a 1k coins as a 100 dollar one you'd get a 100 bucks. Common stuff they'll generally just offer a replacement or like dealer bid price if you want the cash. Rare or loosely traded coins it's more complicated but there's always some back and forth involved and people that don't lose their minds and stay professional generally do a little better