The feeling comming on whilst riding long flat tracks or commuting suggests that the same position is maintained for longer periods, whilst riding other disciplines the Weight change and shift in the saddle and on the bars will differ between shifting up down braking steering and all the other associated actions !
Sitting pedaling holding an object out front with upper body weight exerted onto the heel area of the palm will almost always cause discomfort,
If none of the above works try pedalling so ur legs hurt more than your hands,
And as for suggesting index finger ?
Why not also consider Thumb ?
Could that be Ulnar ?