The problem with Jacob and Leah is that very few details are given. Octoberose says "And how does Genesis say Jacob and Rachel married? "Jacob went into her" after Laban gave her to him." I don't think Genesis is saying that's how Jacob married her, that happens after Jacob marries her.
Gen 29:21 And Jacob said unto Laban, Give me my wife, for my days are fulfilled, that I may go in unto her.
Jacob calls Rachel his wife before he has sex with her. Laban has to give her to Jacob, not unlike God giving Eve to Adam. Adam and Eve had a marriage ceremony, however small and "informal" it was. The sex happens after the marriage ceremony. Traditionally, couples have sex on their wedding night. This is after they're married, not to become married.
So Laban gathers all the men together and makes a feast. Presumably this is a wedding feast. No details are given here. Neo, you state
If the feast/ceremony/vows/oaths had already occurred with Rachel the night before, then Jacob was already married to Rachel. ALL OBLIGATIONS HAD BEEN MET.
Nowhere does it say these things occurred with Rachel. We're given no details. Did Laban give a speech about how Jacob is marrying Rachel? Or was he being vague and only saying how Jacob was marrying his daughter? Maybe Jacob assumed he meant Rachel, since that was what they agreed, but everybody else assumed he meant Leah, since Laban says "It is not so done in our country, to give the younger before the firstborn." Either way it doesn't say.
Were Leah and Rachel present at the feast? We don't know. In the evening Laban brings Leah to Jacob. Jacob doesn't know it's Leah. Maybe she's covered, or it's dark, or both. Only in the morning does Jacob find out it's Leah. Laban tells Jacob to complete the week of Leah, and then he will give him Rachel. This would be a week of festivities, similar to Samson in Judges 14:12-17.
Gen 29:28 Jacob did so, and completed her week. Then Laban gave him his daughter Rachel to be his wife.
Rachel is now his wife and then he has sex with her. Not to make her his wife, she's already his wife because Laban gave her to him.
You mention Bilhah the handmaid and say that no ceremony is mentioned. No ceremonies are mentioned because the focus of these passages is on making babies, the sons of Israel. You bolded the key words yourself.
Gen 30:4 And she gave him Bilhah her handmaid to wife: and Jacob went in unto her.
Bilhah becomes his wife first, then Jacob has sex with her. A ceremony would be understood, since the word wife is mentioned.
Moving on from Jacob, let's go to the Law of Moses.
Exo 22:16 "If a man seduces a virgin who is not betrothed and lies with her, he shall give the bride-price for her and make her his wife.
Exo 22:17 If her father utterly refuses to give her to him, he shall pay money equal to the bride-price for virgins.
Here we have a man who sleeps with a woman who isn't his wife and doesn't become his wife until he pays the bride-price for her and her father accepts. If her father doesn't give her to him, she's not his wife, even though they had sex. A similar passage occurs in Deuteronomy.
Deu 22:28 "If a man meets a virgin who is not betrothed, and seizes her and lies with her, and they are found,
Deu 22:29 then the man who lay with her shall give to the father of the young woman fifty shekels of silver, and she shall be his wife, because he has violated her. He may not divorce her all his days.
This bride-price is mentioned a few times in scripture. Boaz pays for Naomi's possessions and for Ruth.
Rth 4:9 Then Boaz said to the elders and all the people, "You are witnesses this day that I have bought from the hand of Naomi all that belonged to Elimelech and all that belonged to Chilion and to Mahlon.
Rth 4:10 Also Ruth the Moabite, the widow of Mahlon, I have bought to be my wife, to perpetuate the name of the dead in his inheritance, that the name of the dead may not be cut off from among his brothers and from the gate of his native place. You are witnesses this day."
Rth 4:11 Then all the people who were at the gate and the elders said, "We are witnesses. May the LORD make the woman, who is coming into your house, like Rachel and Leah, who together built up the house of Israel. May you act worthily in Ephrathah and be renowned in Bethlehem,
Rth 4:12 and may your house be like the house of Perez, whom Tamar bore to Judah, because of the offspring that the LORD will give you by this young woman."
Rth 4:13 So Boaz took Ruth, and she became his wife. And he went in to her, and the LORD gave her conception, and she bore a son.
Notice there are witnesses. And that only after Boaz takes Ruth to be his wife does he go in to her.
And the other bride-price mention I found is between Saul and David.
1Sa 18:25 Then Saul said, "Thus shall you say to David, 'The king desires no bride-price except a hundred foreskins of the Philistines, that he may be avenged of the king's enemies.'" Now Saul thought to make David fall by the hand of the Philistines.
1Sa 18:26 And when his servants told David these words, it pleased David well to be the king's son-in-law. Before the time had expired,
1Sa 18:27 David arose and went, along with his men, and killed two hundred of the Philistines. And David brought their foreskins, which were given in full number to the king, that he might become the king's son-in-law. And Saul gave him his daughter Michal for a wife.
Earlier Neo, you stated
But I'm not talking about that either. If I claim to be married (per Ray's understanding), I must produce evidence of a vow.
More broadly, you must produce evidence of a ceremony performed in front of witnesses. Nowadays this would be a marriage certificate. In Ray's study, he says "They have found actual marriage contracts, Jewish marriage contracts that go back to the 5th century B.C. So this idea of, ‘well they didn’t have ceremonies.’ Yes they did. In fact Malachi was written about 500 B.C."
Ray doesn't give a source, but I did a quick google search and sure enough, there are references to ancient marriage contracts. I'm not sure if there's any place in scripture that mentions them, but I did find 3 places where certificates of divorce are mentioned.
Deu 24:1 "When a man takes a wife and marries her, if then she finds no favor in his eyes because he has found some indecency in her, and he writes her a certificate of divorce and puts it in her hand and sends her out of his house, and she departs out of his house,
Isa 50:1 Thus says the LORD: "Where is your mother's certificate of divorce, with which I sent her away? Or which of my creditors is it to whom I have sold you? Behold, for your iniquities you were sold, and for your transgressions your mother was sent away.
Jer 3:8 She saw that for all the adulteries of that faithless one, Israel, I had sent her away with a decree of divorce. Yet her treacherous sister Judah did not fear, but she too went and played the whore.
If they had certificates (other translations bill, writing, scroll) for divorce, I'm guessing they had them for marriage too.
My post is getting long, so I'll end here.