Your concept of the circular buffer and method of cracking the MIDI messages seems sound. So what is the issue? I can see no problem of reading a byte at a time out of your circular buffer to construct the message. Or is memory the problem?

Another method is to crack the incoming message in the interrupt routine. You could then store a pointer to the message in a circular buffer.

Normally with MIDI you don't want to introduce too many delays so you want to process the message as fast as you can and pass it on to whatever.