@Freetraveltips,
I am no expert, but I understand that "salam allaikum" means, generally, "peace be with you". The basic meaning of the hand path is: "FROM my heart TO my lips and my thoughts" which is similar to Christian, but in absolutely different contexts, which explains the difference in direction. The "salam" is a respectful salutation to a person before you, meaning that you intend to act, talk and think according to your heart (truthfully). The Christian (catholic) long cross sign is a sigil: the christian "places" the Cross, closing those "doors", over head, mouth and heart. It is a inward path of consacration, a blessing and it is just used in cerimonial contexts towards his god. It is not a salutation, but a sign of reverence, close to the long bow in which the believer kneel down and touches the floor towards Meca (analogous to the genuflection to the cross or sanctum when entering a church in Christian context).
The salam has an answer that is "alleihem salam" ("and with you, peace"), which MIGHT have the opposite direction in movement (I don't really know), meaning that the listener will take his words to heart.
What I have explained here have good basis, considering islamic culture, which places special value in the words of elders.