Does James 2:10 pertain to breaking the whole law while ignoring sin's degrees of severity?
Answer: Your thesis appears correct. The passage from James is irrelevant to any consideration of severity because all sin demands eternal death.
While we might distinguish between a lie and murder, the latter being much worse than the former, such is not the case with God. What we fail to appreciate is that God is an absolutely holy, majestically perfect Being. He can never tolerate sin or imperfection in His Presence.
It makes no difference how small an infraction we think we have committed. When we violate the least commandment of the "Royal Law" or the "Law of Liberty" we have broken the whole of the Christian faith. James is merely reiterating that which Christ pronounced in Matthew's Gospel (5:19). Much of what James writes pertains to the theme of "perfection in Christ."
Most of us know that we cannot, of ourselves, ever attain this perfected state. It requires the blood of Christ to cleanse us, and that is what He does through prayerful repentance and obedience:
1 John 1:7, 9: "[If] we walk in the Light as He Himself is in the Light, we have fellowship with one another, and the blood of Jesus His Son cleanses us from all sin… 9If we confess our sins, He is faithful and righteous to forgive us our sins and to cleanse us from all unrighteousness.
By cleansing us of all sin, and all unrighteousness, we are made perfect. We do this as we reach to God, and He reaches down to pull us up to Him — but only as we obey Christ's commandments. As author and scholar, James Coffman, once wrote:
[This demonstrates] that even Christians who earnestly strive to do the will of Christ are nevertheless not able to attain any acceptable degree of perfection in their own right. The proper respect for this truth will have the practical effect of driving every man to Jesus Christ, in whom alone the perfection required by Almighty God (Matthew 5:48; Colossians 1:28) may be received through God's grace.
As mentioned in the OP, this is "an all-or-nothing" proposition. If someone breaks part of a piece of glass, they have broken the whole; if they snap a link in a chain, they have broken that chain, etc. There are no half-measures in Christ.
What many fail to appreciate is there are many commandments of Christ which are violated when we ignore them, such as baptism, the command to assemble on the first day of the week (Sunday) for worship, the command to partake in the Lord's supper, and so forth. Disobeying or ignoring these vital imperatives makes us lawbreakers. Here, we might consider the consequences for violating these commands in Matthew:
Matthew 7:21-23: “Not everyone who says to Me, ‘Lord, Lord,’ will enter the kingdom of heaven, but he who does the will of My Father who is in heaven will enter. Many will say to Me on that day, ‘Lord, Lord, did we not prophesy in Your name, and in Your name cast out demons, and in Your name perform many miracles?’ And then I will declare to them, ‘I never knew you; DEPART FROM ME, YOU WHO PRACTICE LAWLESSNESS.’"
These are profoundly sobering words. Even those who prophesied, cast out demons, and performed many miracles — all in the name of Christ, have fallen woefully short only to be condemned! We must, therefore, pay attention to the smaller things that some of us might overlook or ignore as "unimportant." This is what James is relating to us in James 2:10.