I'd be inclined to try to enforce her sleeping spots more strictly so she doesn't sleep anywhere other than on a dog bed which is going to cause damage. Yes - teaching an old dog new tricks isn't always successful - but you've got a Lab - and I've never seen a Lab which isn't able to be bribed - I mean trained with food. Have you thought of a crate for when you're not there supervising? But I've never tried training a 13yr old dog.
Winston will head for any dog bed I put - at last count there are 5 or 6 around the house, some left over from my other dog who died last year.
Fortunately he was crate trained young - and when he sees me getting dressed to go out, he goes and lies in his crate ready for me to close it before going out (if it's night - daytime he's got the run of the house and yard - though he prefers to be in the crate, as he knows he gets a tiny treat!!!).
There is a bed either side of our double bed, one near the door, one near the organ and one near the piano. Two of them are makeshift - 4 old Electric Blankets with the plugs cut off and 2 folded on top of each other - I don't think he's worked out that they're not plugged in
I've set a movie camera up while I was out a few times - and he normally settles in the bed near the door (so he can supervise me leaving - wanders to the one near the piano after an hour or so, back to the door bed - never not in a bed.