"This method would keep the attic ventilated but cuts back on the radiant heat coming in from the underside of the roof sheathing".

If you can use a straight edge, utility knife, and stapler, you can diy this for big savings using rolls of radiant barrier. The install is on the underside of the rafters using the rafter cavaties as channels to trap the heat gain and is pushed out by way of the soffit venting up and out the ridge venting. Here's a link to an outfit that offers different install methods and radiant types. I've used 50" wide x 1000" rolls one side foil faced. fiberglass mesh inbetween, with the opposing side kraft paper. You hold it up 3" from where the rafters meets the top plates and run it perpindicular to the rafters overlapping and foil taping the seams. You overlap at the ridge as well. Your soffit/ridge venting must be continous run meaning every rafter cavaty would be vented to allow the heated air to escape. The radiant blocks it from entering the attic. Very effective anvenue of keeping the attic cool.

Here is a link that might be useful: radiant barrier

The effect on the service life of the shingles is the same with radiant barriers as with an unvented foamed roof, about a 10% reduction.

Using foam under the roof decking without turning the entire attic into an unvented design will not be effective. Whether you want to retrofit an unvented design will depend on a number of factors, most especially if you have any services in the attic, i.e., HVAC and ducting. See link.

Here is a link that might be useful: Lstiburek on: Understanding attic ventiliation

My concern using radiant rolls installed as mentioned above would be your high humidity levels. You are essentially turning your attic into a non vented attic with the exception of holding the radiant up 3"' from the plate line which does allow some air intake. The installs I've done are here in the mojave desert where humidity levels are relativaley low. You might want to research what effect the humidity might have by blocking your soffit/ridge venting with the radiant rolls.

Here in the mojave, composition asphalt based shingles have no where near the claimed manufacturers life span due to heat excess regardless. You would be lucky to get 20 years off of a claimed 30 year shingle.

Spray insulation expands when introduced to oxygen. When the insulation is applied it begins to expand to fill in cracks and crevices. This process can produce insulation 5 to 10 times its size when wet.

Why not just add more insulation to the ceiling and maintain the ventilation.

Foam would be more effective than standard batts insulation in the rafter cavaties, both would still allow quite a bit of heat gain into the attic. Radiant reflects and holds the heated air in the rafter cavaties pushed out by the soffit/ridgeventing. You wouldn't want to combine the radiant with any insulation type filling the rafter cavaties as the purpose is to have the rafter cavaties act as channels ,(an air space), for the heated air to gather and be pushed out by the venting. Some radiant installs are similar to the styrofoam baffles that create an air space between the roof sheathing and the insulation below it, but Imo, the whole cavaty as an air space is more effective without the need for insulations, at least here in the mojave desert.

Foaming the rafters will be the least effective way to decrease the cooling costs of your home.

Not only will foaming the rafters cost 3-5X more to install than simply increasing the existing attic floor insulation, it will actually add to the cost to cool and heat your house because the attic will now be required to be heated and cooled.

This adds up to a net perpetual increase in the cost to heat and cool your house, but adding foam in the attic will therefore never fully pay back the inevstement if at all.

Best option is to add floor insulation to the attic, add ventilation to the attic, but more importantly: seal all air penetrations between the attic and conditioned space below by caulking and sealing all penetrations from:

-pipes
-chases
-chimneys
-vents
-attic doors
-etc.

Foaming the rafters will only be a waste of money.

When considering an unvented attic, usually the most important factor is the location of the HVAC system. If all or part of it is in the attic, it then becomes more likely that the extra costs of an unvented attic are outweighed by the ongoing energy savings.

If the system(s) are elsewhere, I second manhattan 42's advice above.