Let me present a concept. Have you or I ever gone through a red light or received a speeding ticket? I know over the years that I have and not always in innocence. The courts are filled daily with traffic violations; however, we do not rationalize that because we cannot keep the law perfectly that we should eliminate the traffic laws; we just do our best. It's the same with Yahweh's laws; we do our best to keep those laws that are not related to animal sacrifices for atonement, since Messiah's perfect sacrifice put those into disuse.
As with King David, Yahweh looks at the person's overall attitude of heart -is this person's heart really one that "wants" to keep Yahweh's laws (and therefore does, the majority of the time); or is this person's heart really just interested in doing things its own way? As we know, King Saul's heart was more interested in pleasing the people and himself rather than obedience to Yahweh. The obvious contrast to King David is given to us for this lesson!
The 613 laws that you refer to have many man made interpretations, such as wearing little boxes on the forehead with scripture inside. I do not recommend using this specific list as a reference. It would be a good start for one to keep the Sabbath and the Festivals of Yahweh that were commanded FOREVER. Then, continue studying the scriptures yourself.
Check this link about keeping Feasts without the animal sacrifices: FEASTS. Paul said, after Yahshua's death and resurrection, to keep the feast; and he kept it without the animal sacrifices for sin atonement. 1Cor 5:8 (KJ) "Therefore let us keep the feast, not with old leaven, neither with the leaven of malice and wickedness; but with the unleavened [bread] of sincerity and truth."