I think the first suggestion is the best and more logical explanation for the alleged discrepancy concerning Joseph's father (the second explanation is also plausible but wouldn't be my preferred choice).
MAT 1:16 And Jacob begat Joseph the husband of Mary, of whom was born Jesus, who is called Christ.
LUK 3:23 And Jesus himself began to be about thirty years of age, being (as was supposed) the son of Joseph, which was the son of Heli.
The Jewish levirate law states that when a man dies childless his widow -
"shall not marry to another; but his brother shall take her, and raise up seed for his brother" (Deuteronomy 25:5).
The child of the second marriage is legally the child of the first (Deuteronomy 25:6).
Heli died childless. His widow became the wife of his brother Jacob, and Joseph was the offspring of the marriage. Naturally the son of Jacob, but legally the son of Heli. It is likely that Matthew gives the natural descendant and Luke the legal.
* Matthew: arranged in eleven groups of seven individuals, and Matthew has deliberately shuffled the data specifically in order to fit the schema (it's not a strict genealogy for purposes of identifying descent); individuals are selected in Matthew for theological reasons
* Luke: arranged in a simple and pedantic 'son of' genealogy but in reverse so that it ends in Adam, part of an extended theme across three chapters which culminates in the temptation; for Luke the entire point of the exercise is to show that Jesus was the son of God as Adam was, but that Christ succeeded where Adam failed (in Luke, Christ is introduced as the son of God in contrast with Adam, and Christ starts with a victory having been led into a wilderness for temptation and ends with a victory in a garden, whereas Adam started in a garden for temptation, and was driven into a wilderness as a result of failure)
Both Matthew and Luke are using genealogical data for a literary purpose, not for a genealogical purpose. Matthew carefully arranges his in a particular order (eleven groups of seven), in order to make his various theological points. Luke similarly uses the genealogical data for his theological purpose, and skips right over Abraham and David without even mentioning Christ as the fulfilment of the Abrahamic and Davidic promises, because he really wants to get to Adam and contrast Christ the son of God who was victorious with Adam the son of God who fell. He also wants to show that Christ, unlike the demi-gods of the myths which his Greek reader Theophilus had worshiped, was solidly real and existed in the world of humans, not the mythical realm of the gods.
Since neither Matthew or Luke is interested in providing a strict genealogical lineage of Christ, neither of them are 'more correct'. They're both arranging the data in a way which is useful to their purpose. Matthew and Luke's genealogies are arranged in two completely different manners for two completely different reasons. Both of them are thematic.