Replace the Pro Mini and USB serial with an Arduino Micro. The Micro uses a 32u4 microcontroller so it has a native USB port. There is a library to send MIDI over the native USB port. No need for hairless.https://www.arduino.cc/en/Reference/MIDIUSBThere are many other boards with the 32u4 chip such as the Pro Micro, Leonardo, ItsyBitsy 32u4, and Feather 32u4. Any one can be used instead of the Arduino Micro.
Yes, a number of changes to source code will be required to switch from MIDI to MIDIUSB.I have never used HIDUINO. I do not know how to solve this problem because you really do need a 16u2 to use HIDUINO.