The pics are a little bit confusing. Normally, you put the shocks on the ground vertically or level out the bottom of them (eye to eye) and do the measure. Then you'll likely see that the level of lower spring seat is the same between the standard and Type R version. But the top hat is lower in the Type R version than OEM, so the whole strut is shorter and easier to mount anyway. That's because the spring wouldn't be preloaded if the strut is fully expanded (changing wheels, autocross
). A loose spring in the strut is not a desireable thing to have and can be pretty dangerous. So the Type R shock has a limited expansion/stroke, realized by a rebound within the shock itself (normally a piece of rubber), maybe 1''. When both cars (NSX-R and OEM) are both off the ground you can see the difference of negative suspension travel very clearly.
Also the Type R spring is not linear initially like the OEM. The Type R is slightly lowered. This is the result of the 3-4 upper windings of the spring going on block (see the rubber? anti-noise...) which results in less resistance/force as the spring begins to compress, so the car sits lower even though the lower spring seat is at the same height as OEM and even though the spring rate is 3x higher than OEM. If both were linear the Type R would be even higher than stock.
Back to your scenario: the needed rebound (not the valving, just the limiter of stroke) of a shock is determined by the desired height AND length of the used spring. The lower you want to go the higher the rebound (in mm) has to be to ensure that the spring is preloaded by >50 kg or 10 mm in ANY circumstances. That's the point to start with. Fit the shock and spring together and screw the top hat on them and see if it's pretentioned enough. You don't know the actual ride height at this time, you only know your preferred ride height. So you have to mount them on the car, drop the weight of it on them and measure your ride height (always from center of the wheel to the fender) and decide what the lowerest height level will be you'll ever want to go. Don't go too low. Then do the calculation.
In my very first run, I've decided to install a rebound of 40 mm, which was a little bit too much for the Zanardi springs. Now, I'm at 20 mm on B6 which is exactly what B8 are. B8 is nothing more than the added rebound of 20 mm. As you might have to send the shocks several times to Bilstein for revalving you'll always have an opportunity to correct the rebound.
The higher the spring rate - the lower the car - the more rebound is needed - the less negative suspension travel. Too low suspension travel is not a desireable thing to have. The wheel must be able to 'follow' a pothole or example.
One more hint: even the Zanardi springs (linear 6.5/5.0) need a rebound of 20 mm front and rear if you install them on the lower perch of a B6 because the springs are shorter. Even more stiffer springs need even more rebound. Now imagine the negative stroke of a combo like 12.0/10.0 TEINs with linear springs...insane.
Hope this helps. As it gets very technical it might be obvious that English is not my mother language.