Since you're headed toward the idea of a live looper for the MIDI control signals, I searched the Kyma Sound Library by Sound name for "looper" and found an example called Four-track live looper on audio input ch 1 to use as a starting point.
In place of the mic input, I used a Constant with !cc01 as its value (as Gustav was suggesting). This will record the !cc01 live input into memory and loop the playback, but it isn't sending it to the MIDI output yet.
For that, you can use a MIDIOutputController from the Prototypes with the looping Sample playback copy/pasted into its Value field.
Here's the MIDI cc Looper Sound in case you'd like to use it as a starting point for your experiments. Since there are four outputs, I had it generate output controllers cc01, cc02, cc03, and cc04 (all on output MIDI channel 1). But you could instead modify it to output all four as cc01, each on a different MIDI channel.
I didn't have a convenient way to test it out but hope it's useful just to get things started. Let us know how it goes!