How do Biblical Unitarians who accept Jesus’ sinlessness understand this argument?

The questioner's logic and conclusion are rational.

Jesus is the first of a new type of humanity.

He is of the next age. He is the new man. He is better in all ways than his predecessor, Adam.

1 Cor 15

21 For since death came through a man, the resurrection of the dead comes also through a man. 22 For as in Adam all die, so in Christ all will be made alive.

We can observe God's character in His design. Life comes from seed and its the Father who sows the seed. A farmer represents our Father.

His garden was infested early on by an enemy. All of the Father's seedlings in this age have been corrupted because they are all of the lineage of Adam.

God our Father loves His Creation dearly. Instead of destroying His garden completely and starting over, He is in the process of saving it. His method for doing this is by planting another seed.

Matt 13

31 “The kingdom of heaven is like a mustard seed, which a man took and planted in his field. 32 Though it is the smallest of all seeds, yet when it grows, it is the largest of garden plants and becomes a tree, so that the birds come and perch in its branches.”

The Father and 1 eternal Farmer produced a second seed of Himself; an incorruptible seed. This seed was used to beget Jesus, His only begotten son.

1 Cor 15

45 So it is written: “The first man Adam became a living being”; the last Adam, a life-giving spirit. 46 The spiritual did not come first, but the natural, and after that the spiritual. 47 The first man was of the dust of the earth; the second man is of heaven. 48 As was the earthly man, so are those who are of the earth; and as is the heavenly man, so also are those who are of heaven.

He is the new True Vine, the conduit for the Spirit of his Father. We as his brethren are grafted onto this Vine in this age making us incorruptible in this new garden - the New Creation. The garden will get tilled after the harvest and the 1 eternal Farmer, our Father will start again. This is the age to come.

John 15 New International Version

1"I am the true vine, and my Father is the gardener. 2 He cuts off every branch in me that bears no fruit, while every branch that does bear fruit he prunes so that it will be even more fruitful. 3 You are already clean because of the word I have spoken to you. 4 Remain in me, as I also remain in you. No branch can bear fruit by itself; it must remain in the vine. Neither can you bear fruit unless you remain in me.

5 “I am the vine; you are the branches. If you remain in me and I in you, you will bear much fruit; apart from me you can do nothing. 6 If you do not remain in me, you are like a branch that is thrown away and withers; such branches are picked up, thrown into the fire and burned. 7 If you remain in me and my words remain in you, ask whatever you wish, and it will be done for you. 8 This is to my Father’s glory, that you bear much fruit, showing yourselves to be my disciples.

How do Biblical Unitarians who accept Jesus’ sinlessness understand this argument?

1. All men are sinful.
2. If Jesus is not God, he is a man.
3. Thus, if Jesus is a man, he is sinful.
4. Jesus was not sinful.
5. Thus Jesus must be more than a man.

Let's assume, for the sake of understanding the final conclusion of this argument, that all of these premises/conclusions are in fact true. We could summarize them with a couple of additional conclusions/premises, as follows.

1. Since Jesus is not a man, he is God.
2. Because he is God, he is not sinful.

There is a hidden, subliminal message to this--one that Satan is keen on every person believing. It is this: only God can be sinless.

If this message is believed, then one cannot believe, or follow, Jesus' command given in Matthew 5:48.

Be ye therefore perfect, even as your Father which is in heaven is perfect. (Matthew 5:48, KJV)

And if one cannot believe (trust) or follow (obey) Jesus' commandment, one does not love him.

If ye love me, keep my commandments. (John 14:15, KJV)

Therefore, to believe the five points listed in the OP is to oppose the teachings of Jesus, and to show one does not love him who gave his life for him or her.

Further, it sets up plain contradictions in the Bible that can be illustrated by the following list of premises.

1. God claims to be immortal (see 1 Timothy 1:17; 6:16).
2. Jesus, who is God, died (see 1 Thessalonians 4:14; Acts 13:30).
3. God says He cannot be tempted with evil (see James 1:13).
4. Jesus, who is God, was tempted (see Matthew 4:1).
5. God claims He does not lie (see Numbers 23:19).
6. Therefore, since God contradicts Himself, He cannot be trusted.

[Lies in italics]

Conclusion

The conclusions reached, if the original premises posted in the OP are followed to their full, show us that those premises cannot in fact be true, for they are self-contradictory.

As a non-trinitarian, I understand the argument presented in the question as invalid. It fails to properly summarize the Biblical teachings on the subject, and ends up teaching a message that is at odds with itself, with Jesus, and with his teachings.

Jesus saith unto her, Touch me not; for I am not yet ascended to my Father: but go to my brethren, and say unto them, I ascend unto my Father, and your Father; and to my God, and your God. (John 20:17, KJV)