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clueless tourist pedestrians wandering (often backwards, holding a camera) across the bike lane
Here in lies the rub. It's a park. People don't expect to get decked by bikes in a park. They don't to expect to have to read signs, either, to prevent them from being decked by bikes when they blunder in to the 'wrong' bit of the park.
This is why Broad Walk is so shit - there is no physical design to tell people that different bits of the 'walk are for different things.
From the plans - first post - it seems that RP are not adding additional physical differentiation to the cycle lane. They are taking what differentiation there was away. At every junction, the cycle path ends, and the space in between is some weird no-mans land with golden gravel where anything goes, including I assume walking backwards with a camera, anywhere you like, which is totally cool - in a park :)
The proof will be in the eating I guess, and maybe the raised paving will do something. Who knows!
Howard-
I think the idea is that the whole route is "anything goes" so people will use their natural common sense (ha!) to avoid conflict i.e., it is based on the original principle of shared space: visibly maximise the theoretical risk and people will compensate and work it out amongst themselves. This seems to work ok in Kensington Gardens as long as you don't expect to cycle anywhere fast.
ffm
I think the changes in Kensington Gardens were a bit of a waste of time and money. There never seemed to be significant conflict on that route since most traffic was end-to-end. Hyde Park seems slightly different, Broad Walk was always an area where I routinely encountered clueless tourist pedestrians wandering (often backwards, holding a camera) across the bike lane (in contrast to the South Carriage drive, which has a fence along its south edge, preventing crossing). Since there was no real acknowledgement of the bike lane (as designated by the white line and bike symbols), giving cyclists a sense of ownership of that lane it seemed to add to the potential conflict and stress. Re-signing it to clarify that it's a genuinely shared-use path across its whole width makes more sense to me. I've never understood whay people would expect it to be anything other than a low-speed lane i.e., a pedestrian area to which cyclists are given access.