同意你說的第一種分析：pedal 是及物動詞，它的賓語是his way，up the slope 屬介詞短語作狀語。這樣的搭配很普通。類似的如：　　

The man pushed his way authoritatively through the crowd.  那個人從人群中硬擠出一條路。　　

He tried to bluff his way through another test and failed it.  他試圖再次在考試中蒙混過關，但卻露餡了。　　

Brand elbowed his way to the centre of the group of bystanders.  布蘭德擠到看熱鬧的人群中央。　　

They tried to handcuff him but, despite his injuries, he fought his way free.  他們試圖把他銬起來，但盡管有傷在身，他還是奮力掙脫了。　　

Seaton pushed his way into the crowded living room.  西頓一邊說對不起、借過，一邊擠過人群進入擁擠的客廳。