Sadly, no.
I'm becoming convinced that TinyCore 9.0.3 just doesn't work on the Pi Zero. It apparently works on Pi Zero W, but that's not what I have. I've even gone to the extent of buying a selection of different USB WiFi dongles, and purchasing the "official" Pi Zero USB hub. I've verified all the USB dongles work fine under Raspbian, which means I also know that the passwords are correct and that they are compatible with the network and the Pi hardware. TinyCore gives exactly the same issue all the time, even when using wifi.sh - it sees the networks, it just refuses to connect.