I like the discussion, but I fear we are loosing people at this point. But I do want to comment:
1. Yes, I have on occassion, on a road I am very familiar with, under traction conditions I know(or assumed and was right, a "calculated" risk) doubled the posted speed for a corner. Not at the entry, but certainly by the exit I have attained 70 mph on a few 35mph posted turns. Once, on a Buell XB12 I managed to hit the rev limiter before exiting a corner in 2nd gear, which I'd guess was in excess of 60mph on a tight right handed turn. It was on a turn posted as 20 mph, probably because the turn had another road intersecting to it, but the sightlines were all clear. It is very possible.
3. No actually, there are many ways to determine an "expected" apex for a turn before getting to the turn entry. Read the terrain in the turn area, read the road slope/camber, read the turn FAR before you get there, perhaps 1/2 mile before in some cases, read the "treeline"; if you see a LOT of trees perpendicular to your direct ahead line of sight, its a tight turn. If you see trees at an angle to your direct ahead line of sight, its a broader turn (learned this in the unmarked turn/twisties of south central Missouri), read the shoudler painted line, read the centerline, read from traffic exiting the turn. READING a turn starts FAR before you ever get to the turn, taking in data that clues you to the turn setup. All that reading before the turn helps set up your apex choice before the entry.
I got caught on a cresting RH decreasing radius turn in Missouri. I did not read the "falling" tree line to clue me when riding uphill to the turn. I got in, it got tighter, and a truck in the other lane. I looked to the exit, maintained speed and pressed HARD on the right grip. Dragged my boot edge, centerstand and my passenger boot edge, and made the turn. My mistake was I did not read the terrain before getting to the turn, but I adjusted and made it. Not to brag at all, but just saying it is possible to adjust.
I'll have to claim ignorance on Grodsky's four second rule for blind corners until I find what was printed by Larry on that subject. Larry was a very competent cycle safety expert, but also a very competent rider who could describe techniques we can really use. Based on what the OP said, "Grodsky's informal tests seemed to indicate 4 seconds was the time needed for good experienced riders to stop in a curve when there were not any road surface problem.". I underlined "time" because as it relates to braking, especially in a curve. Back to 35 mph, or 51 feet per second, if in a curve and the rider had to suddenly stop, 1/2 sec is spent in simply reacting and starting the braking process. There goes 26 feet. A good straight line stop, clean dry pavement, from 35 mph is about 50 feet and about 2 seconds. So we've gone 76 to 80 feet through the turn. Larry is generous with his "four second" guide, taking 1/2 second off for reaction/application. leaves 3.5 seconds for braking, about 1.5 second longer than a straight line stop. So now we're into more like 100 feet to come to a stop from 35 mph.
You easily see the potential problem if the speed at entry is 70 mph. Because braking from speed is not linear to start speed. 70 mph braking is not twice the distance of 35 mph braking. More like four times the distance, especially in a curve. But very few riders consider braking performance in these terms, and fewer still practice any braking skills, until its pucker time.