When you assume that a "different covenant" = "different law", then of course you're going to conclude that the Ten Commandments are no longer valid.
Do remember that if "New Covenant" = "different law", then that means that the rest of the 9 commandments must be replaced with entirely new laws as well.
Somehow, it is convenient for you to only replace the 4th. Unless you will tell me that the 9 were abolished too? I can't imagine you going that far.
The Tables of the Covenant have a law written "on them". The New Covenant is a covenant of the heart, where those same laws written on that Old Covenant Table is written on the tables of your heart.
The purpose of this covenant is to instill in the mind the importance of keeping God's laws out of true love--true faith that produces fruit. The covenant has changed, not the law.
"not according to the covenant I made with their fathers" does not = "not according to the laws", as a covenant is always a "contract", an "agreement", a "pact", a "promise" concerning the laws. The keeping of those laws was based on a NEW PROMISE (not the same kind of promise made with the Fathers).
Continue to interpret that a Covenant is identical to the laws themselves, and you're going to continue running into theological shipwreck.
The Ten Commandments were called the Covenant because there was a contract involved in keeping them.
Let's also not forget that the Tables of the Covenant were given in Exodus 20, while the blood of an Ox for the Old Covenant was not shed until Exodus 24.
This is why the Tables of the Covenant TRANSCEND the Old Covenant, and are "intrinsically tied to the Everlasting Covenant".
This is Perspicaciously demonstrated in Psalms 111:7-10.