Saying any word quite slowly makes it sound quite odd, but the main issue I found with your recordings was that in both of them, the word "cyclists" sounded like you were saying "cyclixts".
I don't agree that it sounds like "s + short pause + ts". When I say those words, the "sts" is definitely one sound at the end. With "cyclists", it almost sounds like "cy + cli + sts".
With the 6 Minute English piece, I haven't finished listening to it, but you are right that it is pronounced differently by the two speakers. The most obvious one so far is when the woman says "Some people think the cyclists are to blame" (I think that was it). She has clipped the word so much that it seems to have no ending at all!