Current status: Can you hook a USB battery up to a cheap solar controller using a 12V-to-5V converter? I looked in online forums a lot and couldn't see anyone saying you couldn't - to be honest, I couldn't see anyone asking either. So. Punk it - 20 quid and some sunshine and let's find out:
60W panel top right, going to solar controller in blue on the right via a DC cable. Then through the converter mid-bottom-left, out through the USB voltage metre in the middle, to the battery bottom-right.
And technically, yeah, the battery still charges. Initial tests show the output from the controller swings around a lot more wildly than plugging the battery straight into the panel, which probably makes sense as we're in unchartered territory? And the panel makes a high pitched noise but I read that that's a common thing cos frequencies.
I feel like it sort of works, but (instinctively?) maybe I'm more likely to kill the battery faster cos of the power fluctuation. And I haven't seen what happens when the battery is full - it should probably shut itself off, unlike a lead battery. The use case is really when the sunshine is patchy, or I want to put the panels out but the sun isn't up yet. Need to run some tests when I'm at home on a partially-cloudy day. Maybe that'll happen now the weather is getting cold and crisper.
On the plus side, still going strong despite a long run of wet weather recently...