Tire / rim data help

Having enough knowledge to be dangerous is a good place to start.
To answer you r questions first: The tall sidewall/low pressure combination is used for more than just an increased contact patch. It also allows for effectively a variable final drive ratio. Giving the highest ratio at low speed/launch conditions and low ratio at high speed (due to centripetal acceleration).
The second question about availability of low weight WHEELS in the sizes mentioned: This is going to be expensive to make happen since the increase in wheel size mandates more material (CART and IRL wheels 15*14 were forged magnesium and weighed in at about 10 pounds, 30 pounds with dry tires). However, keep in mind the WHEEL does not exist on its own, you must look at the weight of the WHEEL and TIRE together. More specifically, the inertia of the two. Basically the amount of weight and how far from the center it is, if you were to take a cross section from the center out. This is not data typically posted by tire and wheel manufacturers and definitely not by re-sellers. If you are looking to get custom wheels, then you should be able to get a number for inertia (assuming the maker uses CAD to desing the wheel or assemble the components).

In my consideration for larger wheels (diameter) there are two things that jump out.
1) Increased wheel diameter allows for bigger brakes. This only makes since if the braking limit of the tires can not be reached by the exiting system. One reason F1 cars still use 13 inch wheels is to limit the braking performance (already at 4+ Gs), bigger wheels allow for more braking power.
2) Increased wheel diameter reduces the sidewall for a given tire diameter. Some of this was discussed above, but the drag race case does not translate to road racing very well, since the drag cars don't impart a large lateral load to the tire. The reduced sidewall will increase the initial steering response by removing some of the undamped tire from the system. Basically the tire (for a given set of pressures/temperatures) is stiffer. Also there will be less steady state (mid-corner) roll in the tire. This will keep the tread under the wheel better and give more instant feedback thru the steering wheel, which may a bad thing on very rough surfaces (requiring you to ignore some of the feedback and push thru it until the surface cleans up or the loading is reduced).
3) Increased wheel diameter genarlly means more cost (exponentially more so if you are looking for a lightweight package). This comes in the cost of the wheel and the tire. the tire cost may not be much more for a single set, but with time the increased cost will add up.
4) The last item to consider is fatigue. Not yours after reading this, but the fatigue of the wheel. Everytime you turn thru a corner, you are adding to the fatigue of the wheels. The same goes for accelerating and braking. For larger diameter wheels of a lightweight design, the fatigue life is shorter than for a smaller diameter wheel of the same weight. Basically due to the amount of material that exists to react all the loads put into it. If you look at the street car wheel market, there is a listing for maximum weight per wheel. This is less about the actual weight than the fatigue life limit. The fatigue life limit for a car under the weight limit is effectively infinite, over and there is smoe life limit that the manufacturer does not want to take a chance on the wheel failing. For this last point the basic thought is bigger wheels should be crack checked more frequently than smaller wheels of the same basic weight.

I hope that gives you enough to chew on while you search for options.
Later, Steve Stafford.

The aircraft design considerations are a little more 'safe' than race car wheels, but I can appreciate the comparison. My degree is Aerospace engineering.

Basically any change to the contact patch reaction (tire/wheel combination in this case) will require at least a look at the rest of the suspension. If you have a way to check the system stiffness before and after a tire/wheel change, then you can try to work out the difference in tire sidewall stiffness. The groups I work with use tires specific to the course being run to remove the effect of varying tire stiffness, when setting up for a track. Some thing as simple a using scale pads and adding significant weight to the axle/car can give you a quick and dirty read on the difference in the tire stiffness (vertical only, lateral requires different loading and restraints). Also the tire pressures will not be the same for different tire/wheel combinations so that addds to the testin/developing scenario.

I did not want to start off the discussion that way so as not to scare you away from the idea of varying the wheel size. To add one more comlication, you could consider different tire/wheel sizes front to rear, in order to tune the limit feel of the car.

Just my 2 cents worth.
Later, Steve Stafford.

I've always gone with the rule of thumb that the smaller the better. Figure out the maximum amount of brakes you're going to need (stopping force and thermal mass), then wrap the smallest wheel you can around them.

I imagine if you look hard enough you can get some test data on certain tires in your size.