NESBA and Yamaha sponsor a ride demo of the R1, R6, FZ1, FZ6R, and a homebuilt WR450F supermoto.

They run four 15 minutes sessions the hour before a regular track day. No obligations. You don't even have to be doing the track day. Phoenix and I sampled R6s last weekend.
Unfortunately there was a crash in each session (and multiple crashes during every session of the track day). With each crash the control riders dropped the speed by 10 or 20 mph and there was NO passing. We barely got the bikes into 3rd gear. 17 bikes have been totaled this year in this program.

I took the chance to ride the R6 because it's been 2 years since I've done track days, and that was at Barber on a 600.
The R6 -- this is not your father's 600.

It is absolutely worlds apart from my 2001 ZX-6R in every way. Power, handling, braking, riding position.
Engine -- I almost stalled the bike trying to pull out in the paddocks. You must rev it to 6000 rpms to pull away from a stop. But get it over 10,000 rpms and... oh!

The bike actually
pulls. Not like an R1 but harder than what I remember from my friend's 675. There really is nothing below 10,000 rpms and the sweet spot is 12,000 to 15,000 or so. This engine would be sooo much fun on the track, and the NESBA guys said it's much stronger with an exhaust system and a power commander.
My old 600 could roll away from a stop sign at less than 3,000 rpms and easily handle traffic at 4,000 rpms. On the one hand, I say I would never use an engine like this on the street. On the other hand, the vibes weren't bad at all and the bike was easy to ride at 8,000 - 10,000 rpms.

People get hung up on the absolute revs, but with a bike that revs past 16,000 rpms, 8,000 is only 50% of the way to redline.
I would definitely be happy with the power on the track where my old 600 felt overwhelmed by the other bikes and any long straight. I liked the throttle response on the R6, but others said it was twitchy.
Clutch -- Almost zero friction zone. Terrible in the paddocks, but easy to grab a gear on the track.
Brakes -- They stop you. No drama and well controlled. But we weren't going all that fast for the track.
Handling -- The bike is tiny. You feel like your hands are in front of the front axle. Somehow though there isn't much leverage, though. Turn in felt just right for a track. Not too light/not too heavy.
Fit -- I'm 5'10" with a 31" inseam and weigh 185 without gear. The pegs felt fine (for the track), but the reach to the bars was way too short. The seat is pitched forward and the clip ons are low so you're either tucking in, doing an extended push-up, or locking your elbows. Only the first one felt good on the track, but then my crotch would slide into the tank. Think "monkey humping a football" in a way that no reasonably sized 600 (think F4i, YZF600R, or ZZR600) would do. When I could slide all the way to the very back of the seat, the position felt ok. The bike desparately needs Stomp Grip pads, but really, it needs maybe 2" more reach to the bars for normal sized Americans.
Would I buy one? Well... sitting on Phoenix's GSXR was a lot more comfortable. The R6 engine is too gutless down low for the street and the GSXR 750 would have a little more power on the track. I'd be curious to ride a GSXR 600. These bikes have really gotten extreme in the past few years. Even the R6 has gotten more compact over the last 6 or 7 years.