Indeed, the moons effect on the seas is very obvious. But the moons orbit is not circular, but elliptical, hence at certain times of year it is closer than others, this accounts for spring and neap tides. Studies have shown that the gravitational influence of the moon affects life cycles in shell fish, oysters for example when taken 1000s of mile from their home shore would open and close in sympathy with the home tides for several days.
I think however that it is doubtfull that the lunar gravity has any effect of closed fluid systems, like us and plants. The effect would just be too weak.
The reason lunar planting was used by the ancients is simple - the moon is a bl00dy big thing in the sky, and watching it over the course of a year is easy. At autumn, the moon is often closest, and optical effects in the atmosphere at low angles make it seem very big. So a big moon like that coincided with the crops being ready, and so is known as the Harvest Moon. Look up native american indian mythology, and you will see they had many different moon names depending on time of year. For instance one that coincided with wild herd movements, when hunting was easy, was the Blood Moon.
More usefull for planting though is the solar angle, a low sun (winter) meant colder temperatures, a high sun hotter climate.
The idea of waxing and waning having any affect is rubbish. Incidentally less powerfull spring and neap tides also occur due to the position of the moon relative to the sun. Waxing and waning simply relates to the ammount of illumination the moon receives from the sun.
Martin