Why would "But" function as its own clause in Hunt's (1965) T-unit and clause system?

I am learning about Hunt’s (1965) system of parsing writing into T-units (minimal terminable units) and clauses. In this system, a T-unit is,

one main clause with all the subordinate clauses attached to it [if any] … An and between two main clauses would always go with the second clause, beginning it just as coordinating conjunctions so often begin the sentences of mature writers.
_{Hunt (1965, p. 20)}

– while a clause is,

a structure with a subject and a finite verb (a verb with a tense marker). If subjects were coordinated, they merely lengthened the clause, and if any part of the verb phrase was coordinated, that also merely lengthened the clause.
_{Hunt (1965, p. 15)}

This system is useful for breaking up the writing of children, who often write long compound sentences connected by and. Hunt provides this example of an essay written by a fourth grader:

I like the movie we saw about Moby Dick the white whale. The captain said if you can kill the white whale Moby Dick, I will give this gold to the one that can do it, and it is worth sixteen dollars. They tried and tried but while they were trying they killed a whale and used the oil for the lamps. They almost caught the white whale.
_{Hunt (1965, p. 20)}

So, Hunt transcribes this into T-units (each on its own line), with clauses split by slashes (p. 21):

1. I like the movie / we saw about Moby Dick the white whale.

2. The captain said / if you can kill the white whale Moby Dick / I will give this gold to the one / that can do it.

3. And it is worth sixteen dollars.

4. They tried and tried.

5. But / while they were trying / they killed a whale and used the oil for the lamps.

6. They almost caught the white whale.

I do not understand why there is a slash after “But” in T-unit 5 – but does not contain its own noun-verb pair, and it seems to me that this but does not have a very different function than and (in T-unit 3). Is there some finer point of grammar that I'm missing?