Black box exceptional groups of Lie type II

If a black box group G   is known to be isomorphic to an exceptional simple group Gˆ of Lie type of (twisted) rank >1, other than any F42(2e) or D43(2e), over a field of known size q  , and if suitable SL2 and Discrete Log oracles are available when q   is odd, then a polynomial-time Las Vegas algorithm is given that produces a constructive isomorphism between Gˆ and G.