r U2 r U' r' U' r2 U r
R r U2 r U' r' U' r2 U r
R2 r U2 r U' r' U' r2 U r
R' r U2 r U' r' U' r2 U r
R2 U' r' U' r2 U r
R2 U2 r' U' r2 U r
R' U' r' U' r2 U r
R U' r' U' r2 U r
r' U' r2 U r
R r' U' r2 U r
R U R' U' r' U' r2 U r
Average movecount: 8.0
Average double turns: 1.6
Algorithms: 12
This is an exhaustive list of all possible edge orientation cases (upto AUF) possible after first block, with 6 misoriented edges; given the edge in DB is oriented. The edges marked green in each diagram are oriented, and the edges marked red are misoriented. The general theme is to place the good edges in UR and DR, and do a quick 5 move trigger that orients everything. Due to partial EO, these cases will be rare.
Note that the final two moves are flexible and can be one of (U r), (U' r), (U r') or (U' r'); all these will solve the EO case. The choice has to be made based on which algorithm will result in the easiest BF case, or to preserve some block that can be utilised in the 2-gen part of the solve. As a rule of thumb, the last move should be such that the bottom centre ends up in the top, and the second-to-last move should be such that a BF edge connects with the bottom centre if possible.