I disagree with the track day. Unless you can rent a bike that you are most likely going to crash, I wouldn't do it. You will probably either lay your bike down or crash it on that track day, so I wouldn't do it.
You will get all the confidence you need by just continuing to ride in the twisties and building up your speed as you go little by little.
You can't just throw someone on the track and expect them to come out a professional, which I don't think that is what people are saying. Buy more likely than not, you will crash your bike on that track day and to me that just isn't worth it.
The reason I say you will crash is that you are already scared to death of the turns now, add speed to that on the track and you have a recipe for disaster.
I'm not sure where you came up with this stuff but one thing I can assure you of is you are dead wrong.
Riders very rarely crash on their first track day. Once in a while someone does but not very often. Some track days come and go with not a single crash in any group.
Just to brush you up on reality, it's the guys who have a few track days under their belt that let their balls overcome their skills that are most likely to crash. It's testosterone that causes most crashes at the track.
First time track guys always start out in the novice group and are led around the track for the first couple of sessions by a Control Rider. This gets the brand new guys acclimated to the track. Then they are closely watched by the control riders to help or scold anyone who rides over their head or who may need help getting the hang of things. Ideal place to learn and much less likely to be injured than on the back roads. Along with skilled riders to coach them, what better place to safely improve?
Also, you will never ever accomplish on the streets the amount of skill and confidence you'll acquire from track time.
I challenge you to attend a track day before you make judgments on the more productive way to improve your skills. This idea you have about crashing if you attend a track day is absurd. I can assure you, one track day will improve your skills more than an entire season of street/twisty time!