Quick update.

It's improving with practice. Not fast yet but getting smoother. It's actually easier when I kick a target like a heavy bag. Maybe because the body knows to expect resistance?

The short answer seems to be to keep practicing your kick. Specific conditioning drills might be more useful at an advanced level but I think my kicking muscles are getting enough work just practicing the kick.

Well said! Practice is the best way to go. It isn't the fastest but its the best.

The short answer seems to be to keep practicing your kick. Specific conditioning drills might be more useful at an advanced level but I think my kicking muscles are getting enough work just practicing the kick.

I agree, this is the short answer. Take the time to break the kick down into its component parts, like sensei8 mentioned. To me, it sounds like your main frustration comes from the initial pivot and chamber, so I'd take the time to focus on that aspect of the kick.

Some very good advice here posted. I would practice this very slowly paying full attention to detail, breath in as you chamber and breath out as your kick is going out slow with little tension. If you do it enough times, meaning a lot! then speed will come naturally.

It is very important where and how you deploy your supporting foot,it always have to move first even if a few inches to give your kicking leg the right support and transmit power to your kicking leg.

Slow is the king in practice time to perfecting technique in any field.