Gert,
You're probably thinking of salve (singular), salvete (plural): "Be in
good health, hail, hello!" That is a verb, and cannot be modified. It could be followed by the name of the person greeted in the vocative case, for example "Salve, Felicissime!" = "Hello, Felicissimus!"
"Saluti" is the dative singular of the noun "
Salus", meaning "
health, well-being". If you were wishing someone well-being, there would have to be a verb expressing your wish, and
Salus would be in the
accusative case, "salutem".
So I don't think your suggestion "Most happy greetings!" is possible.