Or is there a better solution when working with a large set of LEDs like this?
Yes, use addressable LEDs.
Normally these come in a strip but you can get them in individual packages like normal LEDs.
However do not use the Neopixel ones, use the ones known as Dot Star, these are Adafruit names for a specific group of LEDs.
The reason not to use Neopixel ( WS2812b types ) is that it takes precise timing to delver the data to them and this requires that the libiary doing the data transfer turns off the system interrupts. This in turn stops MIDI data being received so MIDI messages are missed. The dot star type do not suffer with such a problem as their data transfer can be interrupted with no ill effect.
Any keyboard with a USB MIDI interface is hard to connect to the Arduino as you need a USB host shield. Keyboards with a 5 pin MIDI interface are simple because these are just serial signals.
Is there a way I could tap into this harness and capture the key strokes on the way to the midi output in order to manipulate it?
There may be but it depends on the entire circuit of the keyboard which I suspect you do not have. However it is doubtful because the USB connector will not contain MIDI data on it, in a form you can pick up with the Arduino.