The best way in, although I can tell by reading your post that you're not going to like this, is to get a secondary PGCE in your chosen subject - in this case, music.
The reason is that there aren't simply enough jobs going in the Further Education sector and if you get a PGCE in post-compulsory education (by the way, some of them do not even come with QTS - Qualified Teacher Status, meaning, for all technical intents and purposes, you're not a qualified teacher even after doing the PGCE) you're limiting your possibilities by 1000%. There are not enough jobs going around in general, let alone in FE, for that to be a smart idea ever, but especially right now!
Also, many FE institutions are actually sixth form colleges tacked on to existing secondary schools.
Now, this is where common sense comes in.
If you go for an interview at a FE college attached to a secondary school, and you have a post-compulsory education PGCE and can only teach the 16-18 year olds and then someone comes along after you who has just as much experience as you, a good CV, and interviews just as well, but they can also teach lower down the curriculum and take lessons with the under 16s... be realistic here, who do you think they will choose? I would say 96%+ of the time they will choose the other person who is more flexible (assuming you're equal or near enough in every other way).
So not only are you limiting your teaching options by saying I want to teach FE - which is limiting enough, but fair enough, I completely understand your preference as I share it myself, though with a different subject - but then you're also limiting yourself because when you DO get an interview at an FE college, you don't have that flexibility of being able to teach other key stages should the need suddenly arise (the other music teacher might go on maternity leave, or be on sick leave for a month etc etc.).
Basically... secondary PGCE in music is the best way in, EVEN if you only ever want to/end up teaching at post-16.
I want to be a sociology teacher at post-16 (AS/A2). I plan on doing a secondary social science PGCE that will give me QTS, and allow me to teach sociology at GCSE, AS and A2, as well as citizenship and RE at key stage 3. I don't want to teach RE or citizenship, but I am fully aware that saying I can only teach sociology at AS/A2 will more than likely lead to several years without a teaching job. I do not see the point in doing teacher training, if I cannot get a job teaching, and have to work at ASDA for 5 years.
Making yourself more employable should always be the goal - don't make yourself less employable if you can help it, and, right now, you can!
Like I said, I understand not watching to teach in schools so much, I am the complete same, but in life there are compromises and other things that sometimes you have to work with to get to where you want to be. Some people aren't willing to make them (there's an infamous poster in this education & teaching sub-forum who comes to mind) and thus will probably never be a teacher. People don't just walk in to teaching jobs these days, like every other sector, it's tough. Keep your options open from the go and then you have the options of narrowing down later on. It doesn't work the same in reverse.