I really do not want to be a "spoil sport" but I feel I have to be one?
If you are placing all of your belief upon some family tree posted with the LDS Organization / Church, then you need to understand (if you are not a LDS member yourself) that members are basically required to submit a family tree to the church to fulfill what I believe is a "requirement" for good standing within the church, so one's (your family) family can be made members of the LDS church even though they are long dead!
This, of course, along with a decades old desire of other families to find their "roots" has led to a plethoria of fake or unresearched family trees! Yours is quite likely one of them, I am afraid!
As regards the surnams Paulus or Saulus, certainly I can guess that both of these names merely mean Son of Saul and Son of Paul, thus both are given names with what I consider either an Italian / Latin or other Romance spelling! Certainly in Scandanavia Paul might well be used as a surname spelled Paul-son / sen, or even Pauls!
From a common baby name site;
"The boy's name Paul \paul\ is pronounced pahl. It is of Latin origin, and its meaning is "small". Popular Roman and medieval name used commonly since the 18th century. Biblical: the apostle evangelist. Paul's letters to early Christians form the majority of the books of the New Testament. The name is also borne by Sir Paul McCartney and the pope who headed Vatican II. Pablo is a Spanish form; Paolo is Italian; Paulino, Paulo are Portuguese; Pal, Poul are Scandinavian; Pauel is Dutch; Paulus is Latin; Pavel is Slavic; Pavlik, Pavlo are Russian; Paulson is English; Paulsen is Dutch, Scandinavian.
Paul has 26 variant forms: Havel, Paavo, Pablo, Pal, Paolo, Pasha, Pauel, Pauli, Paulie, Paulin, Paulino, Paulinus, Paulo, Paulos, Paulsen, Paulson, Paulus, Pauly, Pavel, Pavle, Pavlik, Pavlo, Pawel, Pol, Poll and Poul."
The meaning of Paul is usually considered to be "little, small, etc.!" Thus one could have "Peter the Great" and "Paul the Little", etc., if "paul" was used as a descriptive word, and only later taken as being something else, like a surname for example!
So, according to theory, each person with the above names might also claim lineage!
Saul is considered a Hebrew name, and thus is much more limited. Of course there is also that mysterious Biblical name conversion? IE, Simeon becoming Peter; Saul, Paul, etc.!
So, in my humble opinion, your chances of being related to a (semi) historical person at best, is basically nil!
If you researched the beginnings of surnames, you might find out that in most of the world they are relatively a new idea, one used only out of necessity to seperate a world of John's, Peter's, Mark's, etc., from one another. Usually this was encouraged or impressed upon the people by tax collecters, etc. I hate to get this involved but at one time in England for example, in a large villiage there might have existed fourty or more men named John! Thus one was John the Tailor, another John the Black-smith, another John the Forrester, etc., etc.! In this manner you might well see that (almost all) surnames were mere creations, and only have any degree of reliability after it was made necessary to have one!
In one example, it is entirely possible that there once existed some king named Alexander (which means "defender of man") who was very big, tall and fat? In some societies (German?) he might well have been called Die Grosse or Grosser!, or in others The Fat?, etc., but in modern history books he might well be called "The Great?"!
Thus, I would suggest that surnames cannot preceed time periods much before what ever period of time one might consider real census records were required?
© Charles N. Pope, US Library of Congress. All rights reserved.