yup. that's the "problem"...finding a class in which your car can be competitive. honestly, the ES/P5 is a fantastic HS car, but will not do so well in other classes (for many reasons). for example, an LSD will put you into SM, where in Philly, you are running against wicked fast WRX's. definition of own3d.
my advice if you are seriously trying to compete in solo II is stay in HS. first get some R-compounds (Kumho Ecsta V700's will fit the stock rims). cat back and adjustanle dampers (but NOT springs) will also help, but as you have seen, the driver is where most of the improvement lies. get some tires and practice, practice, practice.
PAX is an indexed list of all drivers where your best time is multiplied by a factor according to class (e.g. STX's factor might be .825 while HS's factor might be .755). the idea is to compensate for the car's ability and list the best drivers of the day. you can usually do well in PAX b/c the HS multiplier is pretty good. often, those results will give you a decent idea of your relative standing and improvement.