There is clear evidence that the Haslams manipulated the economics of the second tranche, ensuring that Berkshire would have to pay a lot more as a multiple of cash flow, paying almost 3x as much per share for the next 41.4% ($8.2b) as they had paid for the first 38.6% ($2.8b). After acquiring the second tranche Berkshire had a majority, and was able to make sure this didn't happen again. We don't know exactly how much Berkshire paid for the remaining 20%, but Berkshire thought it was worth $3.0b.

From the Q1 report:
"In January 2024, we acquired the remaining noncontrolling interests in Pilot for $2.6 billion, increasing our ownership of Pilot to 100%."

So, the second tranche implied a total value of $19.8 bn (41.4% for $8.2) but the final tranche for 20.0% implied a total value of $13 bn.
The negotiations for the exact number for the final tranche may have included an implicit credit for the high second tranche, so the "value" may be higher than 13, but presumably under 20.

As an aside, the "expensive" second tranche required Berkshire to record a non-cash gain in Q1 last year because the transaction pushed notional fair value above equity method value by $3.0 bn. It's unlikely that they will have written that back down again.

Jim