I played SD JBs from the 80s, 90s and a current one which came stock in a guitar. Even though I did not try them in the same guitar they shared two predominant characteristics: bloaty midrange and overall muddiness. While I did not yet have the chance to play all BKPs none of the models I tried had the JB characteristics in the least.
Andy Timmons has a very warm sounding bridge tone which is not too overdriven. Hence I think Crawler is a very good choice. Hope you like it!
Cheers Stephan