Most sites block by IP (or IP range), so a direct connection using the
exit node's IP should give you very similar results to a Tor circuit
using the exit node's IP.
Thanks teor! The point still stand though even though my solution to it is flawed. The thing being measured will be friendliness towards the Tor Browser instead of Tor overall. Basically, the measurement will be "friendly to Tor but not the Tor Browser". If that's the intent, then there is no real issue. I don't know how many sites will render for a Tor exit node but also only have issues with the Tor Browser itself but I'm definitely interested in seeing that data.
-Ryan