I did this to simplify the math
You simplified it too much. The first 30% of dawn and dusk do not require accumulators, because they are producing more than 42kW.

accumulator.png
If you cut out the green regions, it reduces the accumulator power needed to only 100 seconds, not 125.

Now I see ...

This is wrong, do not even bother to read it

You are forgetting that the day/night power graph isn't a square wave

100%--- ######## ########
# # # #
# # # #
# # # #
0%---####### ######## #######
but rather has nonzero time to transition between day and night
100 ...

This is wrong, do not even bother to read it

The calculations for 0.16 (and the wiki) are wrong and there are more solar panles than you need.

=-=-=-=-=-=-=-=-=

Day time: 291.67 (1250/3) seconds
Night time: 125 seconds

Solar panel max power output: 60 kW
Accumulator capacity: 5000 kJ


- Now we ...