How much chassis stiffening needed?

I don't know how useful the torque boxes are, I personally don't think much.
Weld-in subframe connectors at a minimum!
For a driver, not expected to be on the track much, a rollbar/cage is a pain in the neck. HOWEVER, if you do have 550hp, and enough suspension to hook it up, you will not be legal to race without one, and certainly not on dragweek!
The alternative is a full cage, tied everywhere possible, including the front suspension towers, BUT, with a removable swing out side bar.
With an added nitrous system, I would use a fixed side bar.
(I tend to have NO respect for guys with obvious mega power...... and no bar or cage. Pro fairground poser!)
With a proper five point harness, used EVERY TIME, and proper nhra legal rollbar padding, I don't wear a helmet on the street.
Just seen a video yesterday with a 64', 1,300 HP Comet, missing everything you mention here. $204,000 and 23 years invested and only a lap belt. First time out he rear ended a SUV at a red light, due to brake failure. Both occupants were severely injured. Had they had a harness they would of been fine injury-wise, financially, no.