The fundamental problem at the moment is that we haven't found a repeating sequence in these sounds.
...We know that there is some pattern to the sequences; never the same sound three times in a row...
I don't know about this. I think there are effectively two tracks of audio: The Purrs & Chittering, and the Howls. The Purrs & Chittering
never overlap with each other, and the spacing of the two different Purr tones seems to be extremely regular. There are cases where a Purr gets overshadowed by a Howl, and you need to subtract the Howl to be able to hear/see the Purr. That being said, a few of the Purr transcriptions (to binary) that I've seen put spaces between strings, I'm assuming where the Howls come in. That might not be the intention of the being creating the code...and it might be hindering our translation. If the Howls aren't part of the Purr message, and you run the Purr data stream continuously with no spaces, you DO get cases where there are three Purrs of the same type in a row. It also removes the oddity of how there seem to be several 6-bit streams of Purrs in certain messages, especially in UA2.
Also, since the timing of the Howls and Purrs seem to be out of synch, perhaps the ratio of their repeat intervals is significant. Or perhaps the (eventual) synching up of a Purr and one of the Howls acts as a start bit, or 'leading punctuation' indicating the start of a long message. Perhaps the message is so long we assume it doesn't repeat, and it just requires several jettisoned recordings to get the whole message. I'm a little late to this game...how long are the longest recordings?