Thanks for the further clarification of "cop some stick." Bob Watson just sent me further clarification and speculation himself:
"Your translation of the phrase "Cop some stick" is accurate enough to be going on with. The word "copping" does also refer to being caught at and arrested for some misdemeanour, but in this context in tandem with "stick," it implies acquiring something unwelcome, such as blame and dislike from other parties. Stick means verbal punishment or abuse. Could be its roots lie in London East End (Cockney) rhyming slang, where the actual rhyming word is omitted from the equation and its spin off link-word left in situ. eg Butchers equals butcher's hook equals look. . . . or Brahms equals Brahms and Liszt equals had a drink or two too many . . . . ."