Unfortunately, your car is only eligible for stock/street category through this year; as the sunset rule dictates the 30 previous model years from current as allowable. This doesn't appear to be of concern to you, however, as there is no sunset rule for the other categories including Street Touring and Street Prepared.
More to your point, Solo II classing is rather unique because of the lower speed and largely transitional elements that occur on course. Yes, power has a significant impact(moreso in recent years as course design has evolved and speeds increased), but given the unique elements on a course other factors weigh heavier there than on a proper road course. The torqueband, gearing, weight, wheelbase, suspension geometry, and many other factors have greater influence than peak power in solo. This is why you find 25-30 year old Hondas outrunning new pony cars on course with 4 times the power and 5 times the tyre.
Most cars don't spend much time at peak power on a course, but rather in the middle. This is why some of the less 'hot' models are actually more competitive than their racier(and usually peakier) counterparts for solo competition such as the Celica GT vs. GTS in GS, the base Miata vs. MazdaSpeed Miata in ES, and several others. Peaky motors are less than ideal for solo. Because of this and the fact that multiple layouts compete with one another(Evo/STi vs. S2000 and Vettes in BS, Minis and WRXS in DS, etc) Solo event performance has a lot of course dependability. I'm not going to go further into that as it would be quite lengthy, but the existing classing is largely data driven on averages and new models are classed by committee.
When I say data averages, I mean performance averages. Using the BS S2000 vs. C5 Vette comparison; the Vette gains somewhere upwards of .1 for every 100ft of acceleration range, but the s2000 picks up about .050 at each slolam cone. Given a fair and average course design, the theory is that the two should finish about the same time. Of course, if you find yourself running a course full of 1st gear pivot cone digs followed by 300ft straights with one slolam; you will almost certainly lose to the vette. Now, if you find yourself on a course such as described above, I would simply request a refund and go home and mow the lawn. Screw that. Darlington is a a difficult site to design a course for given the long and narrow lot, so you will find it only gets better as you run more events around the area.
As for the specifics regarding HS(and GS), I'll illustrate some history on stock/street classing. In recent years there have been some massive changes to the stock category in solo.
Just a few years ago stock class allowed R compound tyres, open exhausts past the catalyst dumping behind the driver, while banning not stock diameter wheels, adjustment of suspension beyond factory ranges, and many other little things like shift knobs and badging. Scca has strived to open the classing to a broader range and as such banned r compound tyres, allowed +/- 1" wheel diameters, opened sway bar allowances and alignments a bit, while removing restrictions on non performance items like badges and knobs. In doing so, this altered the parity in various classes as cars that were 'the car to have' on race tyres became also rans. I'll leave that at that and if someone wants to discuss further we can.
The other side to the changes made were the introduction of the sunset rule, and classing reorganisation. The scca is trying to make the street class more accessible by making the 'car to have' in each be readily available new at the dealer. To do this quickly, they aggressively classed a few newer cars that completely obsoleted(sometimes only in perception, but that's all that is needed to instigate change) some of the older, less accessible cars to have. HS was, a few years ago; home to a perceived single dominant car that was relatively expensive, didn't sell in huge quantities in the option package, unreliable, and ate a set of Hoosiers before breakfast. The car to have in ES was a 20+ year old car in an option package that was only built in the 100s, and the car to have in BS was a $35k car they built 699 of for two model years(66x one year, 3x the next). There hadn't been a true original 'legal' ES car on the grid in years; they were all clones. Now, the downside to this is that entry level costs for the most entry level of classes is now a car loan/lease plus prep. Reasonable minds may differ as to whether this was the right move for the sport.
Conversely, because of the massive skill differential you'll see, especially at local events, these deficits can be overcome. For what it is worth, my car makes 91ft-lbs of torque at 7600rpm on 6 inch wheels and weighs within 100lbs of the Fiesta ST. When I do attend solo events I compete with the Fiesta. I do have the benefit of a real suspension, narrow chassis, and lower centre of gravity, though. It's also the best looking car in grid, and that matters when your car is slow because people have so much time to look at it on course.
Every region has the ability to dictate their own variations on SCCA rules for their needs(some banned R comps years ago, for example), so that can vary from region to region. Nationally, FSP does not have any wheel or tyre width limits, only that the tyres are DOT certified.
As for the speed adjustments; in full prep that is about correct. When I ran DSP I was in a 2.5RS on 15x10 wheels with 275/35/15 Hoosiers, and although the motor was stock internally the gains from the suspension adjustments and wheels/tyres put the car regularly on pace with the same Vettes described above. With much less weight in the Corolla and equally poor suspension, I would expect similar times.
Unfortunately, the Corolla would be in STS along with God's Chariot and the Rainbow Roadsters. Tough crowd in there with proper suspensions, but it's been done before as recently as a few years back with a 240sx in class.
The gentleman with the F20 powered AE86 in SM is classed incorrectly. SM allows engine swaps, but only from the same manufacturer. For example, you can put a RB25 in a 240SX, or a 13b in a Miata, but you cannot put an LS1 in an RX7 because GM did not manufacture any engines for that model. However, you can put an STi motor in an FRS because it was a joint venture between Toyota and Subaru(Scion is recognised as Toyota for this purpose). Again, individual regions are allowed to have their own exceptions to the rules, and in some classes there are agreements among competitors not to protest others for various items so there may be something else at play.
Edit: I don't find myself here very often anymore, but if anyone has any questions or such I'll be glad to help in any way I can.
plenty of modifications have happened in order for me to get below the roll bar, and even then it's still a little iffy. 
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