Okay, you've made improvements to the offending lines, but let's see if we can get things down to an even more basic level.
Drawing closer to the tree he saw the sun drop behind the plains,
Approaching the tree, he saw the sun drop behind the plains,
If there's a synonym for what you're trying to say that will save space, use it.
He lifted himself slowly to avoid any scrapes or signs of his detour.
He lifted himself carefully up the tree.
Here again, I just switched out five words for one reasonable synonym, and I cut out the last part of the sentence as unnecessary.
When he reached the highest branch that could support him, John felt the night air grow colder.
At the top of the tree, John felt the night air grow colder.
In this case, you want to write from a functional perspective. What I mean by that is that in your story, the highest branch that can support him is the top of the tree, practically speaking. Unless there's some significance to him not being able to get to the literal top of the tree, you might as well call it such. Especially if, once again, it will save you space.
After lifting his coat from the tree without causing any further damage John picked up the brown paper bag of bread, milk, and cheese and returned to the road that would lead him home.
This sentence is fine, but I want to draw your attention to the structural aspect of writing. Not only can descriptions become boring, but form can as well. Many of your sentences start with the verb first, and then that verb is applied to the subject. This creates a very specific sound and rhythm in a written piece, as this can lead to longer sentences. Writing that way is fine, but you want to mix in varied sentence structure and length to keep your reader on his or her toes. Think of every punctuation mark as a stop sign. If you're in a car, and all the stop signs are the same distance apart, it would quickly become a boring ride.
In the same way, you want to vary the pauses and breaks in your writing to prevent the ride from becoming boring. Consider the difference between these two sentences:
After lifting [<=verb] his coat from the tree without causing any further damage John [<=noun]
John [<=noun]lifted [<=verb]his coat off the tree, careful to avoid damaging it.
The technical term for what I'm describing here is
Subject and Predicate. The subject in your sentence is always the noun (in this case, it's John), and the predicate is always the verb that describes the noun (in this case, it's the verb "lifting").
In most of your sentence structures, the predicate precedes the subject. This isn't wrong, but when done enough times, it forms a pattern in your writing that can become boring to the reader. Try to avoid that habit in the future by mixing up your sentence structure.