A bit of data logging showed a single 1W panel useful for supplementing battery power to my mesh network node, but not really enough to charge it meaningfully at the same time. My garden is south facing and the house blocks direct sun lots of the day so it was only the few hours where the panel was in strong direct sun that the result was acceptable. For something that spends a lot of the time asleep this would be reasonable but as I want each node to run for all the waking hours then I need it to do better. I did get 52 hours of runtime, which is technically enough for my needs if I fit two 18650s in the node, but I still don't like the thought of it running down constantly with only a tiny amount of headroom.
The data also shows the regulator board I took out of a drawer is an LDO, not a buck converter, so it's 60% efficient a lot of the time. I will make a pin compatible replacement with the converter I specified for the final boards and that should be a big help.
I've now set up two 1W panels in parallel to make an effective 2W panel. Only a few hours later it's clear this makes a massive difference as they spend lots of time charging the cell rather than just 'treading water'. I'll leave the test to run until the battery protection kicks in at 3.5V but it looks like 2W panels really are what's needed even if I were to replace the LDO. There are some really quite affordable 2W 5.5V cells on Banggood, so going up in size isn't a big deal.