Had another watch of the vids... Here's my 2p (sorry if any of this is 'teaching your grandma to suck eggs' type stuff!):
Seems like a lot of the understeer is under steady state cornering or the exits? 'Slow in, fast out' works well here, if you go in understeering the temptation is to keep the power on and the steering lock applied, so you just understeer all the way through. If you get all your speed off before the corner, turn in later, apex later, your exit from the corner will be in a straighter line, so you can get more power down without understeer (and a higher speed at the end of the straight). Imagine there is a string from your steering wheel to throttle pedal - 100% throttle = 0% steering possible, 25% steering lock = 75% max throttle, 70% steering lock = 30% max throttle, etc. Your tyres can only do so much work!
Similarly, if you do start to get understeer, lift off a bit and straighten the wheel up, that should get the tyres gripping again - you may run a bit wide initially but it'll still be faster/smoother than understeering out and having to get off the throttle at the last minute.
You can also balance the car with the brakes (weight transfer) - throttle = shifts weight back, brake = shifts weight forward. More weight on a wheel = more grip. So if you get on the power too early in a corner, it shifts the weight back, less grip on your front tyres, understeer, you put more lock on as you're panicking about running wide, car ploughs straight on and you have to get off the power just at the point you should be applying throttle.
Trail braking can help... if you brake towards the Apex (but get your downshifts and most of your speed off in a straight line first) it will leave more weight on the front wheels, and therefore more grip, better turn in, meaning you hit your apexes better and can get on the power earlier, without understeer. Similar thing to the throttle though - more steering lock = less braking possible without locking up, so as you wind the lock on, reduce pressure on the brakes. Note: some people think this is 'dangerous' and 'not to be tried unless you are an expert' - personally I found it very intuitive, and easy to get the hang of, but approach with care as too much braking will have you swapping ends!
You can see the difference here:
http://www.youtube.com/watch?v=dRFFM44SQTQ
Lap at 3:00mins, no trail braking. Laps from 6:15 with instruction, started trail braking. You can hear there is less understeer, and I ended up about 1s quicker on the lap
Oh, and keeping your hands on the wheel at all times should help too, so you constantly have full feeling what the front wheels are doing. Crossing your arms is better than 'feeding' the wheel for track stuff.
Some semi slick tyres will definitely help you carry more speed though, more grip and stiffer sidewalls:
PS: This is all my experience, if anyone disagrees then that's fine - more than open to some discussion!
