Ok. I will weigh on this one. I am a Viper Owner, licensed instructor, drive/instruct at Summit Point, and just finished both racing and instructing this past weekend at Charlotte/Lowe's in-field road course (the original part of the thread).
Let me be the first to say that all instructors are not equal. I am firm believer that you should really try to match up with guys who drive the same type of car that you drive. This past weekend I had a tricked out Cobra R and Z06 for my students. the idea is that I am more in tune that a front wheel drive guy is likely to be. I also usually tell the students when I first get in the car not to be bashful if my style doesn't match theirs: everyone is different and they have paid they money and should get the best experience they can. You need to speak up and quiz your instructor on what they have done and what they want to teach you. DON'T BE BASHFUL - I am convinced that the industry runs off plenty of potential students.
I get a giggle when Viper/Ferrari guys show up at the track. Unfortunately, we often reinforce the image of a Viper owner being a wealthy guy who doesn't listen. A lot of Viper guys think their car is the be-all-end-all and that all the instructor wants to do is drive this hot car. Yawn. Most instructors are scared to death of driving a student's car. In most cases, we only do it if the student is having real trouble. But sometimes, the instructor can save you a TON of time on the learning curve. This weekend my Z06 student was doing okay, but not great. He asked if I would drive his car during an instructor session and take him out to show him the line. We did and this bright guy gained in a few minutes what would have taken him days if I had been in the right seat. It doesn't usually work that way in all truthfulness, but with the right student, it can really help.
Now, let me tell you about the part that wasn't great this weekend. A friend of mine was a student with another instructor. He brought his 993 Porsche - a pretty decent car. He really wanted to argue with the instructor and kept saying that his car needed a different line from what the instructor was showing him. In short, a typical high performance driver thinking that the sweaty instructor didn't know how to drive his car. His wife really wanted to take a ride on the track so I took her in the Porsche and promised I would tell him if the line worked. (The regular line worked fine.) After cruising a few laps at around 160MPH, I backed off and came around at about 140MPH when the right rear tire suffered a catastrophic failure. We were just inches from the wall entering NASCAR turn 3. I stayed out of the wall and got us back to the pits, but the defective race tire caused about $20K of damage to the car. If it had happened to him, it might have totalled the car. But it happened to me and I felt miserable all weekend.
There isn't a reason for an instructor to drive your car at the very edge (except in rare situations where you practice braking. Braking, not breaking.) You can learn the line at pretty slow speeds.
So the bottom line is that an instructor can help you learn very quickly when they drive your car. Don't be bashful - ask for a different instructor if yours doesn't match up with you. A mismatch doesn't mean personality flaw on the part of you or the instructor (I have made students go to other instructors because I didn't think my style was as effective with them.) Before they drive your car, make sure that you know their experience. Finally, ask them if they intend to reimburse you if they overdrive you car. At the very least, it will keep the instructor in the right frame of mind.
So, back to the topic at hand: driving ovals. First, ignore the ovals. Just drive them for fun, but don't bother to drive them at the edge. You shouldn't have any problems if you stay close to the white line, but I just can't see where it makes that much sense to take a chance at those speeds. High speed banks are just good for car control and you can learn that on the infield. Have fun on the banks, but don't try to get to 150 or so. 100-120MPH should be _plenty_ fast on most tracks. If you do get close to the edge, hold a little throttle. You don't want to lift since it causes lift throttle oversteer and can send you up the bank.
Don't waste your time left foot braking either unless you are going to do it all the time. (Since you have a synchronizer, you probably won't.) I like to teach students car control, the line, and then braking. The in-field courses are typically pretty tight: they don't lend themselves to the heavy Viper as you try to power around the track. Those Miatas and BMWs will gain on you in certain portions of the track. It's ok.
Have fun. Stay calm. Remember it isn't a competition.