Koji is one of the most wonderful things. It makes amazing things from shiokoji, to miso, sake, to amazake. Just fantastic!
If the miso isn't sterilised, it may be possible to get some spores. I think it will be a challenge.
Koji spores at a warm temperature whereas miso is fermented at quite a low temperature. There is also a lot of salt in it to prevent the koji from sporing. However, if there are air pockets in the miso when it is stored, the koji does tend to grow there.
Actually, the more I think about it, the more possible it may be.
If I was trying this, I would try spreading some miso on a plate, maybe about 1/4 inch thick, keep it at room temperature for a few days and see what kind of mold grows on it. Koji starts white and then goes green when it's ready to harvest for spores. If your miso does that, then scrape off the green mold, dry it, then attempt to culture some koji rice.
The easiest way I found to get koji spores is to buy koji rice at my local Japanese food shop. This is usually in the frozen section. I didn't know the first time that I needed to keep it cold, and I put it in the cupboard. When I went to use it, it had turned green.
Raven, this is just to let you know that the miso test seems to have proved negative. I began on the 19th May, and there has been no change at all to the miso. I decided to buy the Art of Fermentation and I am now perusing the info ... Great book!
Anther possibility is to put some miso in a jar, but leave some air pockets near the bottom. Put it in the back of the fridge for a few weeks. If mould starts to grow in the air pockets, then you could take that and try to produce koji spores from it.
I think you'll love Katz book. Catching wild koji looks pretty easy.
I have begun to read Katz wild koji info. He implies that one can spontaneously manifest the koji spores on rice, once his simple instructions are followed. But I am a little confused by his use of the word 'inoculate' (page 299 line 5). What does he mean? What is to be inoculated? And by what? Does this spontaneously happen with no added item such as a purchased koji starter (which is the reason why I am looking into this - to initiate a homegrown spore)? Or do I still have to buy something?