Would not the social and canonical contexts of Lev. 19:34 in effect have implied the goy "sojourner" in question would either have been a proselyte or at least submissive to the Mosaic laws of the land to the extent that such person would knowingly and consistently have avoided causing native Israelite neighbors and associates to become unclean by means of transference via the goy sojourner himself (at least after a probationary period as a novice talmid of sorts)?
And is not the social and religious context of Acts 10:28 chiefly concerned with Jewish social interaction with goy members of an occupying nation over which Jews in many cases had insufficient authority to ensure at least such minimal compliance with Mosaic cleanliness laws as (per the above) assumed in Lev. 19:34?
Granted at least, your above claim constitutes a warning, and very likely in individual cases outside the Peter-Cornelius events, your point is well made (cf. "the good Samaritan" pericope). But can we wholly separate observance of actual Mosaic cleanliness laws from mere oral tradition (cf. Jubilees 22:16) in Peter's Acts 10:28 concern? How far with respect to Mosaic cleanliness laws can we press Cornelius's (and his household's) reputation among Jews prior to Peter's "sheet with animals" vision (of Acts 10)?
Israel was intended to be a light to the nations in order to draw people to God (Deuteronomy 4:5-8, Isaiah 2:2-3, Isaiah 49:6), yet at the same time they were told to have a holy conduct that sets them apart from the nations. So there is a balance between letting no one see your light, letting your light shine, and exposing yourself to the nations so much that you are no longer set apart, and I think that a law that prohibits Jews from visiting or associate with Gentiles does not meet the balance that God intended for them to have. So while it is rooted in how they thought the Mosaic Law should be obeyed, it was a man-made tradition that actually served against it. Furthermore, it was this man-made tradition that Paul called Peter out for following in Galatians 2.
In regard to Peter's vision in Acts 10, it says that all kinds of animals were let down, so why didn't Peter simply kill and eat one of the clean animals as God had commanded? Why did he object to doing what the Mosaic Law permitted him to do? The issue was that there was a man-made ritual purity law that said that kosher food that came into contact with something that was unclean became defiled/common/ritually impure (Mark 7:3-4). All the animals were bundled together in the sheet, so all of the clean animals had been in contact with unclean animals and had become common. By saying that he had never eaten anything that was common of unclean, he was saying that he had never violated either that man-made ritual purity law or God's dietary law, and by refusing to obey the command to kill and eat, Peter was disobeying God to obey man. Note that God did not rebuke him for referring to clean animals as unclean, but to referring to clean animals as common, so his vision had nothing to do with unclean animals becoming clean, but was in only regard to the status of clean animals. Peter interpreted his vision three times and not once did he say anything about unclean animals.
Granting as you write that "living by faith has always been about trusting God enough to live in obedience to His commands," was "the purpose" the Law was "instructed" for the one who lives by such faith mutually exclusive of another "purpose of" the Law as "so that the sin might increase" (Rom. 5:20), notably among those who do not have faith, but who rather seek their own justification by works of the Law? There is also a difference, is there not, between Adonai's purpose(s) of the Law and the purposes of the people who profess to observe the Law in their use of the Law. Granted, "the Mosaic Law was never instructed [by Adonai] for the purpose of becoming justified [esp. in Rom. & Gal. sense]" if I understand you aright. I think of Isaiah, who was called to prophesy "lest they ... understand with their hearts and turn and be healed" (Isa. 6:10, cf. John 12:38-40).
I think that Romans 5:20 is not speaking about God's Law, but rather it is introducing the concept of the law of sin or the evil inclination. In Romans 7, Paul was said that God's law was not sin, but revealed what sin is (7:7), that it was holy, righteous, and good (7:12), that it was the good he sought to do (7:13-20), the good that he delighted in doing (7:22), and that he served with his mind (7:25), but contrasted that with a law of sin that stirred up sin to bear fruit unto death (7:5), that held him captive (7:6), that produced all kinds of covetousness and gave sin its power over him (7:8), that caused him not to do the good that he wanted to do (7:13-20), that waged war against the law of his mind (7:22), that held him captive (7:23), and that he served with his flesh (7:25). So I think the law being described in Romans 5:20 and Romans 6:14 accurately fits the description of the law of sin and does not at all fit with God's holy, righteous, and good Law.
I think the phrase "works of the law" refers to a third category of law. There is no definitive article in the Greek, so it literally translates as "works of law", which means that it can refer to any laws and does not refer to a specific set of laws, such as God's Law. Paul used it as a catch-all phrase to refer to a large body of Jewish oral laws, traditions, rulings, and fences that they taught were needed to be obeyed in order to become saved. I think this understanding of the phrase is also reflected in the Qumran Text 4QMMT.
In Romans 9:30-32, the problem was not that Israel failed to obtained righteousness because they did what God commanded them to do and God gave them faulty instructions, but rather the problem was that they pursued God's Law legalistically as though righteousness were by works instead of pursuing God's Law spiritually as though righteousness were by faith, as the Gentiles were doing. In Exodus, it ends with God's glory descending the the tent of meeting and with the problem of noone being able to approach and Leviticus begins with God calling out instructions for how to draw close to Him, so Leviticus is essentially instructions for how to draw close to God, and that is the meaning of the root word for "korban", yet people can outwardly obey God's Law without drawing close to Him our of faith and love, and thus completely miss the whole purpose. In Philippians 3:8, Paul had been keeping the Law stringently, but had completely missed that the whole purpose of the Law was to grow in a relationship with Messiah based on faith and love, so he counted what he had been doing as rubbish. In Romans 10:4, Paul was saying that a relationship with Messiah is the goal of the Law for righteousness for everyone who has faith.
