With the large number of LEDs you are using, you could easily run out of memory depending on the complexity and how efficiently your code is written. You might consider upgrading to something like an Arduino Due, which has much more memory at 512 KB when compared to the A-Star's 32 KB. However, the Arduino Due operates at 3.3V and the APA102C LED strips operate at 5V, so you would probably need to do some signal conditioning (e.g. using a logic level shifter) to safely use them together. Another option might be the Arduino Mega. It runs at 5V, but has a bit less flash memory at 128 KB (although, that might be enough depending on your application).
As far as the problem with programming your A-Star 32U4 Micro, can you try following the instructions under the "The uploading-before-bootloader method" heading in the "Reviving using the Arduino IDE" section of the A-Star 32U4 User’s Guide? When you put the board in bootloader mode temporarily in your video, the COM port changed from COM4 to COM5. You should be able to get it to program by selecting COM5 while it is in bootloader mode, waiting until it exits bootloader mode, then clicking the "Upload" button and putting it back into bootloader mode when the IDE shows "Uploading...". It might take a couple tries to get the timing down.