It's a tough call on my Cup tires, not hard from heat cycles but not a ton of tread left either.
On our tires the tread grooves only exist to assist in helping with WET traction. They do this by keeping water from building up under the contact patch.
With a new tire as you go around a turn the tire tread blocks stretch(aka squirm). This is more noticable on an all-season tire with a deeper tread.
Less tread depth = More grip because there is less squirm. Squirm is undesirable because it makes the tire less predictable and causes less overall grip.
Tread "wear bars" exist only to tell you that once your tires wear down to that point that they are no longer "safe" to drive in the rain.(according to dot.)
I personally rock my tires untill the cords show...
Tirerack actually offers a tire "shaving" service in which they shave a specified amount of tread off of your tire with the purpose of deliving to you a better performing tire for competative use.
http://www.tirerack.com/tires/tiretech/techpage.jsp?techid=67&
http://blog.tirerack.com/blog/motorsport-messages-from-marshall/tire-shaving-available-at-tire-rack
Bottom line, A tire with its tread wore down does not have less grip because of this. Rather, the less grip is a result of accumulative heat cycles which firm up the tires compound.
How many heat cycles is too much? Some people just go by feal. Other invest in a rubber durometer and take measurments periodicaly to see how much they firm up over time.
http://www.longacreracing.com/products.aspx?itemid=1618&pagetitle=Durometers
I had one of these handy tools but unfortunately dropped & broke it...
I do not recommend running INVO's on the track. The sidewalls are soft and will excessivly roll over on the fronts.
Nitto NT05 is a different story though. Stiffer sidewall, great for twisty backroads, autox, & track.
Goodluck @ your trackday.