I used to just let the fruit sit on the trees through the winter until they were very soft - almost rotting - and then you could knock them off the trees and catch them in a bag quite easily. But there are too many hungry critters here who will eat the fruit once it is ripe (particularly how they are so obvious once the trees have dropped their leaves). One year I just left a ziplock bag full of fruit out on my bonsai bench - thinking it would naturally cold stratify - but something chewed into the bag and started eating the fruit so I moved it into the fridge.
Personally, I would avoid the soil trays, and keep them in a ziplock bag with a moist paper towel - with water and a little 10% hydrogen peroxide (to eliminate any fungus risk... which I do with any seeds in the fridge). Every couple of weeks check the towel to make sure it is moist - not soaking wet - but otherwise much easier than dealing with soil issues (mold, mildew, etc).
Here is what a tray of this year's seedlings looks like. I just counted, and even though it doesn't look like much, there are 32 in there. The seeds germinate in May... I can't seem to accelerate the process.
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