Some stock to be sold was stacked on a long table, so, after setting the books aside, I dragged it to the wide middle aisle in the central area.

This sentence consists of two clauses:
some stock to be sold was stacked on a long table
after setting the books aside, I dragged it to the wide middle aisle in the central area

“after setting the books aside,” is just an adverbial phrase — not a clause — as it has no subject and no verb. The participial phrase “setting the books aside” acts as a noun. Long adverbial phrases at the beginning or middle of a sentence do take commas, so I recommend writing:

Some stock to be sold was stacked on a long table, so, after setting the books aside, I dragged it to the wide middle aisle in the central area.

You could also use a semicolon before “so”:

Some stock to be sold was stacked on a long table; so, after setting the books aside, I dragged it to the wide middle aisle in the central area.

The second sentence is also a compound sentence containing two independent clauses:

In there I found much of what I needed, but, most importantly, I found boxes of dehydrated camping meals.

Independent clauses:
in there I found much of what I needed
most importantly, I found boxes of dehydrated camping meals

Here, “most importantly” is an adverbial phrase, not a clause, and takes commas. Because “in there” is a short adverbial phrase at the beginning of the sentence, its comma is optional.

In there I found much of what I needed, but, most importantly, I found boxes of dehydrated camping meals.
In there, I found much of what I needed, but, most importantly, I found boxes of dehydrated camping meals.

The last sentence is a true complex-compound sentence, provided we interpret “though” as “but”:

The shop was badly damaged, though once he scrambled through the rubble, he found a storeroom at the back.

Independent clauses:
the shop was badly damaged
he found a storeroom at the back

dependent clauses:
once he scrambled through the rubble

In this sentence, “though,” which usually acts a subordinating conjunction, here works like “but,” a coordinating conjunction. “Though” usually means “in spite of the fact that,” as in,

The shop was badly damaged though the central beam was three feet thick.
The shop was badly damaged in spite of the fact that the central beam was three feet thick.

If your sentence were using “though” to mean “in spite of the fact that,” we would have:
The shop was badly damaged though he found a storeroom at the back.
The shop was badly damaged in spite of the fact that he found a storeroom at the back.

But I think what you really mean is

In spite of the fact that the shop was badly damaged, he found a storeroom at the back.

which could either be written as:
The shop was badly damaged, but he found a storeroom at the back.
or
Though the shop was badly damaged, he found a storeroom at the back.

Back to the whole sentence and your punctuation question, we don’t put commas between two conjunctions unless we would insert a pause when speaking the sentence aloud. I recommend writing:

The shop was badly damaged, but once he scrambled through the rubble, he found a storeroom at the back.

I don’t know that there’s a difference between British and American English punctuation rules for complex-compound sentences, but there may be a difference in the use of “though” as a coordinating conjunction. I’m sure I’ve heard “though” used as a coordinating conjunction in informal speech, and perhaps that usage is more widespread, but I can’t find a usage manual that mentions it.

Some stock to be sold was stacked on a long table, so, after setting the books aside, I dragged it to the wide middle aisle in the central area.

Some stock to be sold was stacked on a long table so, after setting the books aside, I dragged it to the wide middle aisle in the central area.

Some stock to be sold was stacked on a long table, so after setting the books aside, I dragged it to the wide middle aisle in the central area.

In there, I found much of what I needed, but, most importantly, I found boxes of dehydrated camping meals.

In there, I found much of what I needed but, most importantly, I found boxes of dehydrated camping meals.

In there, I found much of what I needed, but most importantly, I found boxes of dehydrated camping meals.

The shop was badly damaged, though, once he scrambled through the rubble, he found a storeroom at the back.

The shop was badly damaged though, once he scrambled through the rubble, he found a storeroom at the back.

The shop was badly damaged, though once he scrambled through the rubble, he found a storeroom at the back.

The shop was badly damaged; though once he scrambled through the rubble, he found a storeroom at the back.

In the last set of sentences has the subordinating conjunction ‘though’ the joining power, if you will, to connect this complex sentence to the simple sentence that precedes it or is a coordinating conjunction required?

Finally, is there a difference between how the British and Americans punctuate compound-complex sentences?