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ORIGINAL: Lee Willis

If you've owned 11 f-bodies and dragged raced for years, then you know very well how much HP it will take to get the car into the tens.  The least expensive way to get there would be to add NOS: withlarger injectors and a 150+ dry kit, and good re-programming, and good rear tires, you'd get there.  Remember that NOS has a slightly cooler/less impacting burn than normal air/gas and thus this method will provide the lowest stress on your stock (and marginal) lower end.
  I'd install headers: a cheap way to get a bit more power. 
  Then, a supercharger would do the trick.  Even with your high compression, you can run enough boost to put the car into the high tens, I'd think.  Magnusen units won't do (they won't blow enough air for a 427 without overreving them): if you want a roots/screw type you'd have to go with a Kenny Bell unit (about $10K plus you have to find a really big-bulge hood..  I'd recommend a Procharger D1SC (one size up from the standard 'vette P model, or the Vortech equivalent, and would not recommend the F (another size up -- harder to fit). 
   As to drag radials.  You can check around but I would think a set of 345s would fit in the wheel wells.  I run 345x18 BFGs drag radials all the time -- street and track.
  Do realize that Lingenfelter has a point in their recommendation: they like to rebuilt the lower end when they add that much power for durability.  With either of these mods, you will be right at the limit of what you can expect to last reasonably long (if you don't abuse it), and you won't be able to push to the lower tens without a built bottom end.  
  I'd also ask Lingenfelter what they do to reinforce the rear end on C6s: they are3 a notorious weak spot on really powerful modded vettes, and an aggresive launch at 600 RWHP can rip them apart.