A little bit of info here back in July 2005

Google gives a tantalising snippet And finally, our Wellerism probably shows contamination with another and quite unrelated Wellerism, "'Aha,' she cried and waved her wooden leg. ... at
JSTOR, but the site tells me I am not authorised to enter. Perhaps you can find someone who is.

More frustratingly Google lists this site which will not open at all for me. It appears you've been looking longer than you thought, Marg: Bak in 1994 Marg Meikle asked about a bit of doggerel/nonsense recitation beginning "Aha, she cried, and waved her wooden leg," and in March of 1996 ...

The various quotes you give seem to have inserted the phrase into a variety of sources:

• "but the villian he still pursued her" sounds like a typical Victorian melodramatic monologue with Sir Jasper or Ruthless Roderick or their ilk
  
• "and the price of timber went up" feels more like one of Billy Bennett's comic monologues of the inter-war years.
  
• "at last I have been satisfied." brings to mind the bawdy student/rugby Engineers Song (a version in DT as THE GREAT WHEEL)
  
• "It was on the bridge at midnight" is a fusion of the well-known parody of Casabianca "The boy stood on the burning deck, his heart was all a-quiver. He gave a cough, his leg dropped off, and floated down the river"
  
• "Aha she cried in accents wild and waved her wooden leg aloft Tis false tis false and with her evil eye she swept the garden path" is in the style of Thomas Hood's Faithless Nelly Gray - "Ben Battle was a soldier bold, And used to war's alarms: But a cannon-ball took off his legs, So he laid down his arms!" Or possibly "Miss Kilmansegg and Her Precious Leg".
  
• And Charles Dickens seemed to be obsessed with wooden legs. Perhaps it's from one of his works
  

Best of luck with your search