When you have enough feeding points you can get away with thinner wires to the boards.
You can also have thicker “rails” wires running alongside and at each feeding point just attach a thinner stub wire to actually power the strip.
By feeding points, are you saying having multiple power supplies which feed power to the long LED strip at various points in the strip?
See drawing: Would this work? (even though all wires are thin)
That’s one option - but all GND of these have to be connected to eachother.
The other is fewer bigger PSUs and have their power distributed via beefier cables from which you “splice” off your stubs as indicated above.
Like in this picture, would all GND be connected to each other, just by way of each LED strip being soldered to each other??
That should do as long the current flow won’t be too much for the GND traces on the strips.
Do I need to provide power to the entire strip before powering the microcontroller?
Because I was planning on plugging in power at farther parts (farthest from microcontroller) of the LED strip AFTER powering the microcontroller, but the GND wire started overheating and melting when I had plugged in the microcontroller power supply (and only this power supply) first.
Does plugging in power at the end of the strip first stop the GND from overheating?
You need to have all the LEDs powered before lighting them otherwise as soon the controller starts lighting the LED strips the current will be drawn from wherever it’s present.
You need to allow for enough time for all PSUs to provide good power before engaging the lighting scenes.
I don’t think this needs a degree in EE but only common sense 
haha thanks.