Well I agree with part of your post, and I know this may be the first we have agreed on anything.
I believe the law is just a generic term, it could mean the Ten Commandments it could mean from the law of Moses, the context will tell us which law is being referred to because Paul will often just say law, so the context will tell us the law being referred to.
Galatians does mention the Ten Commandments, but most of it is about circumcision
For example:
Gal 5:19 Now
the works of the flesh are evident, which are:
adultery, fornication, uncleanness, lewdness, 20 idolatry, sorcery, hatred, contentions, jealousies, outbursts of wrath,
selfish ambitions, dissensions, heresies, 21 envy,
murders, drunkenness, revelries, and the like; of which I tell you beforehand, just as I also told
you in time past, that those who practice such things will not inherit the kingdom of God.
This is similar to what Jesus taught in Mat 5:19-30 where these feelings i.e. hatred, contention, all lead up to breaking God's law.
Anyway, I agree with you regarding there was a law between Adam and Moses because where there is no law, there is no sin and agree the goal post was moved.
Anyway, I just dropped in, I will let you all carry on.
God bless!