The new falken (RT-615) is the fastest tire you listed, in a test run by grassroots motorsports.
buy the August 2005 issue of GRM, they tested the tires worth testing for autocross. No flamefest necessary.
But they still won't be as fast as dot-r's.
They also tested dot-r tires, the slowest R tire was faster than the fastest street tire (the falken RT-615) by nearly half a second (0.44x).
Also the article was interesting in pointing out the characteristics of each tire, which could help with a decision to go with a certain tire for your needs and fitment.
The 712's are the low end of performance tires, a decent tire for the street at a low price, but not comparable to other serious autocross tires. I ran them in 225/40-18 on my Audi A4 and was happy with their performance for the price, but they are no where close to the RT-615's I ran in 225/45-17 in grip levels nor even the old falken RT-215's (the predecessor to the 615) that I ran in 205/55-16.
For slightly better performance (IMO) and also a good price for a performance street tire than the 712, check out the falken GRB415 - but again this is a tire not up to par with other autocross tires - great for a moderate-high level of grip on the street. I ran the falken grb's on my Audi a4 in 225/45-17 on the street and at the track and was very pleasantly surprised with their bang for the buck performance. Not bad at all. They held up pretty well to my overdriving/overheating poor driving at the track.