Verb-ing modifier succeeding relative clause

My instinct is that the 'displacing' modifies the 'sap giving mouth sores to cattle.'

"The rock star threw his guitar to a girl in the front row, who learned to play it over years of intense practice, becoming even more talented than the musician who gave it to her."

There's just too much space (and too big a verb) between that comma,--ing and the initial clause to justify the 'jump' to it, I think.

Is that always the case? Probably not:

"They won a huge victory against the team that was expected to win the tournament, sending them to the championship."

I think the 'that' modifier is 'quick enough' that the last modifier can still describe the main clause.