Ha! Looks can be deceiving. It has gone from 5 corners needing to twist to 3 corners needing to twist to 2 corners needing to twist, but how I got from one to the next? No idea! I can twist 2 corners using R, U, F, and D. I can twist 2 corners using R, U, and D. I can twist 2 corners using R, U, and F. But how to do it using only two faces?!?
Wow. Using Sune to orient corners worked, so now the corners are solved. But the orange edges are double swapped! After different combinations of EPS and Sune, now all the corners are solved again, and 3 orange edges are cycled.
With the Big Block at the lower left, 2 consecutive Sunes cycles edges R to L to B, and twists corners FR and BL anti, and FL and BR clock. R' U2 (RUR'U') x 2 U2 R cycles edges R to F to L, and twists corners FR and BL clock, and FL and BR anti. Solved!
(RU R'URU' U'R') x 2 (U2 R' U2) (RUR'U') x 2 (U2 R U2) is a pure 3-cycle of edges! R to B to L.