Thanks to all for replying. It was a 2 person job but for a different reason than suggested.
My wife and I tried the "one person operates the slide while the other one "pulls like h..." We had zero success with that,, even though, as noted, the slide does tip up (from interior perspective) as it is extended. But while she was still inside I went outside, pulled the lower rubber seal down and shined a flashlight in to see if I could see what the rug was hanging up on.
She saw the flashlight ("honey, I've never seen a light there before"
) and was able to direct me a bit until I saw the bunched up rug.
In the slide fully extended position the rug was easy to touch from the outside but I didn't have any tools with me at the time. I returned today with a bunch; I was either going to free it by brute force or cut it into pieces.
My first idea worked. I brought the slide in about six inches, reached past the lower seal and grabbed an edge with a pair of channel locks. By carefully pulling edges whenever one appeared I was able to mostly "unbunch" the rug. Returning to the inside I gave it a tug and out it came.
Small note posted next to slide control now - fold rug before retracting.
Thanks again to all!