I’ll start a new project thread when I have something more interesting but I can verify your IR sending code works on a Spark Core without any modifications.
Here is the start of my project: https://github.com/edalquist/ac_ir_control
The IR recorder code is directly from your blog.
The IR sending code is slightly modified with some extra debugging and a safety check for bad IR code data.
With those I managed to capture the on/off button from the remote with an Arduino Uno and then replay that signal to control the AC unit with a Spark Core.
One question I have with the recorded signal, can any sort of rounding be applied? My current approach is to capture the same signal a bunch of times and then average each value.