Regarding the 2 genealogies of Jesus, the ESV study bible says that most probably Matthew missed or skipped some generations for example 3 generations between Uzziah and Jotham, and he structured the genealogy in sets of 14 for ease of memorization, or literary or symbolic symmetry. It mentions that according to the Jewish practice of 'gematria' the giving of a numeric value to the consonants in a word, David's name would add to D + V + D or 4 + 6 + 4 = 14, and David is the 14th name on the list.
As for the genealogy of Luke vs. that of Matthew, it says that few comentators today believe that they trace Mary's vs. Joseph's ancestry...so it seems they both refer to Joseph's. Matthew focuses on the royal succession, Luke brings out the actual physical descent.
Regarding the 2 different people named as Joseph's father (Jacob in Matthew, Heli in Luke), most scholars believe they are 2 different people. One solution is that there was a second levirate marriage, so Joseph was physical son of one and the legal son of the other, so there are 2 lines of ancestry...the 2 men didn't have to be brothers but relatives.
Another solution is that Heli was Mary's father, but there were no male heirs in the family so Heli adopted Joseph as his "son" when Mary and Joseph married (similar cases 1 Chron 2:34-35, Ezra 2:61, Neh 7:63)
Before anyone dismisses these solutions, I'm pointing out that the OP asked about any thoughts and I think these among others might be plausible explanations.