Season's End

An intriguing headline (subheadline, really) I noticed in yesterday's Guardian:

(1) "Men's tennis completes its most successful season despite losing in the NCAA Division II tournament."

It's a wild scopal resolution problem, I think. You can't conclude a season despite losing in a tournament. The loss in the tournament is the event that causes the season to end. I think you could say something like "Florida completed its season despite winning the NCAA basketball tournament", but that's questionable to me. And there are certainly cases where "concluding a season despite losing" can happen:

(2) "College of Charleston completed their season despite losing in the Southern Conference Championship."

Where, had they won the championship game they could have entered the season-ending tournament, and given their showing the conference tournament, one might have expected them to be selected for the season-ending tournament, thereby continuing their season.

But in (1), the despite clause doesn't make sense modifying "completes its most successful season"
- unless we read it as modifying "most successful season". Surely this sentence is relatively fine, though:

(3) "It was our most successful season, despite losing in the tournament."

Is this a general fact, that despite clauses can modify either the VP or NP? These sentences seem to support NP-modification by despite:

(4a) Bill ate a satisfying meal despite eating day-old pizza.
(4b) Carl satisfied his obligation to the mobsters, despite only smashing a couple storefront windows.
(4c) Davida finished her paper despite typing it on a computer.
(4d) Zillah pruned the topiary despite using dull clippers.

But this still strikes me as a bit odd.