foxmoth, take your second example. What doesn't happen is that the air at 1,000' remains at 8 C until the surface temp reaches 16 C and then suddenly everything pops off. What happens is that once the surface layer temp reaches 11 C you have an unstable layer below the inversion. Any warm air that detaches from the surface will rise until it hits the inversion, introducing warmer air to the bottom of the inversion. The cold air that sinks to replace it is soon warmed by contact with the ground. This is an ongoing process.
Once the surface temp reaches 12 C, the 1,000' temp will be 9 C, when the surface reaches 14 C the 1,000' temp will be 11 C & since the temp within the inversion is 10 C the unstable layer is now up to 1,330'. When the surface temp reaches 15 C the unstable layer reaches up to 1,660'. So the ELR below the inversion remains at 3 C/1,000' as the day warms.
Hot air rises. One thing that stops unsaturated warm air rising is if the ELR < the DALR, once the ELR = the DALR the warm air below swaps places with the cold air above. Hot air next to the ground can't lift off in one go leaving a vacuum behind it, so you can get a super adiabatic layer close to the ground as the air heats up faster than it can lift off. I have never, ever seen a sounding with a layer of air
detached from the surface where the ELR > the DALR.
Here's a link to a screenshot of yesterday's 1100Z sounding from Herstmonceaux. You can see the super adiabatic layer close to the surface & an unstable layer from about 400' to 2,000', nowhere else does the ELR come close to the DALR.