Cute feet Simon...grins! I think you hit it on the head, too much water, too little drainage. The thyme seems to be trying to thrive. I am thinking your edging might be making a dammed up area and causing poor drainage. That thin metal stuff or plastic stuff? If you were to remove that edging give a little fertilizer to your ground covers...they might just take off.
I'd take a rake and rake it all so there is not separation between chips on your bed and gravel of this walkway. Wait to see how the thyme reacts. Depending on the thyme we should be able to figure out the best ground covers for this area and those that share the same needs to plant together for variety/fun.
If it remains wet we'll probably talk about Speedwell, if it gets drier we can think about Portulaca and Woolly Thyme. I would remove those edging things no matter what. Distracting, look dangerous like knives, they aren't doing any function and I think that it is causing poor drainage, yes, even within a couple of inches of the surface.