Can you find another good example with this combination of verb tenses, Marius? I admit that that sentence logic here needs a little convoluted thinking, but I cannot see it as reading other than:
Mr. Harrington will have been working for 2 weeks by the time he eventually finishes the report.Future perfect references relative past in the future-- that is, a future point from another point farther in the future. '
Finished' puts both actions into the absolute past, since 'report completion' postdates 'work time'. The time does indeed depend on the other verb in the sentence. The only other possibility I see is Conditional:
He would have been working...by the time he finished.