That one's a cooler hack because it runs in old awk, from before they supported user-defined functions. The whole read-eval-print composition is a straight-line series of loops, with the recursions unrolled into explicit stack manipulation. If you want to see how to write fairly readable code within those restrictions, it's instructive. It even has a cooler name. (I said so when bringing it up in my documentation.)
On the other hand, awklisp has some value as a readable Lisp interpreter in a lower-level but still reasonable language, in between the usual Lisp-in-Lisp and Lisp-in-C tutorials.
Yep, that's pretty much how you have to do it. (If all you need is increment/decrement, though, you can actually do it pretty concisely with decimal-digit strings. Skipping the binary-to-decimal conversion greatly simplifies displaying numerical values.)
The GNU sed manual has examples like that at the end. It always seemed odd to show examples of things that are so awkward and inefficient. If they meant for sed to do those things, presumably they would have made commands for them.
More sed fun: http://aurelio.net/projects/sedsokoban/