And no, even the spikes aren't close to 600mA.
The thing is that (I guess obviously) the solar panel is not big enough to successfully power both a step-up convertor and Wemos, so the Voltage drops under load (at least under the current lighting conditions).
And again, before people are again trying to nitpick, first do some testing and measure the actual current the panel is able to deliver, before trying to find a cure to power a Wemos from it.