Jordan said that channeling was the result of a recessive gene, and that the Aes Sedai have been very efficient at removing the men who developped the ability from the gene pool, thus the drop from 3% to around 1% of all human now having the ability. He said that the spark was much, much rarer than this.

You're right though. He did also state the soul of the person has a role in channeling. I had forgotten that, though Jordan never went into details and explained if the ability itself results from a combination of genetics + the right soul, or if for instance the ability itself is strictly genetic but aspects of it such as strength, inborn affinities etc. are determined by the soul. He rather spoke generally that channeling itself was determined by both soul and genetics.

The fact the transmigrated Forsaken have the exact same strength and seem to have all the same talents and skills as before suggests it's all tied to the soul, not to mention some Forsaken (like Demandred, Mesaana) seem to take for granted they should have the same strength after a soul transmigration in a different body.