I’m a newb as well, approaching the 1 year mark now. My process has been almost exactly what you described (minus the TAXI membership) and it seems to be working thus far. Write write write, submit submit submit, all the while paying close attention to what works and what doesn’t work.
One thing I try to do, which I think will prove quite fruitful in years to come, is to forge as many relationships as I can with others in the industry (library owners/reps, media producers, other composers, etc.). I try to be prompt and polite in emails, and I’ve had informative and enjoyable phone conversations with some publishers/libraries.