Without the lock mechanism attached to the back the cylinder should be free to turn in either direction, with the key that is easy to demonstrate, in which case it will pick in both directions.
What could be happening is that the first pin to bind anti-clockwise is the last pin to bind going clockwise and, it is a really low setting pin which just by inserting the pick is being over lifted. This is especially true when long key pins are towards the front of the lock. Very light tension and extreme care when using the pick might be enough to find out if this is happening.
There is also the opportunity to use top of keyway tension instead of bottom for a bit of variety. Top tension can help a lot trying to get under long key pins to shorter ones behind because it frees the bottom of the keyway for the pick to travel along.
The third option besides the lock not operating in that direction and already achieving an over lift on a binding pin is that sometimes when applying bottom of keyway tension the wrench actually snags on the bottom of the cylinder and digs in against the warding, giving the impression rotational force is being applied where actually it's just digging in or pushing up against the warding. One way to test that is to pick the lock clockwise then hold the back while you put the wrench in as if to go anti-clockwise, if it binds instead of turns after you've put some pressure on and released the back, that'll be the problem. Again, top of keyway tension can eliminate possible binding of the wrench against the bottom of the cylinder.
Hope that helps, keep at it
