Could Henri Farman have steered his plane with ailerons on January 13, 1908?
I would first check to see if the car in the background was actually pulling him along in 1908, or maybe the aircraft engine was a bit better.

Banking does indeed reduce lift, but not as much as we may think:

If vertical lift at 0 degrees bank was 1000 lbs, a 20 degree bank at the same AOA and speed still produces: $$cosine 20 degrees × 1000 = 940 lbs$$ of vertical lift, easily corrected by slightly increasing the Angle of Attack of the wing.

The reason the plane previously could not make the turn can be explained by the relationship of thrust and drag.  Turning increases drag, which will slow the plane down.  These early aircraft were very draggy and underpowered, barely getting off the ground.

Deflecting the ailerons (really 2 halves of a speed brake) increases drag.  The bank additionally decreases lift.  With no reserve power to add, the plane goes down.
What an accomplishment the first circle must have been at that time!

But "skidding" the plane around the circle, with rudder only, presents the whole side of the plane as a dragging surface, there for is not a better solution.  The "coordinated turn" using  both rudder and ailerons produces the least amount of drag, and remains the recommended aircraft turning method to this day.

But even the best method of turning requires more power (thrust) than straight and level flight.  A few more horse power, and/or a lower drag design wins the prize.

Reducing weight and a better prop design would also be helpful.