No no no, boats don't travel on land !

(not yet I mean...

)
It's only the tail drawing that is not accurate when running aground.
The tail goes into the ground up to where the boat should have sailed the next iteration if no land.
The next point of the tail is where the boat was the first iteration minute after sailing again.
You can try with it the demo boat or your boat. Put some schedule points to run aground then to sail again in another direction. Refresh each 10 minutes but don't touch the settings, you'll see your boat running aground, but staying on the coast at the exact place where it ran aground, then start sailing again; but you'll notice that the tail goes a bit into the ground, as in the picture you posted above.
This is a minor cosmetic bug, and there is no plan to fix it, although I must admit it can be a little confusing.
(For the record: we had - a long time ago - a hard time setting a working coast detection and boat positioning after collision, but it is now 100% efficient)
About what led you to run aground, you are right, the new winds at the wind shift must have been lower or with a less favorable angle, thus slowing the boat.
In this case (when not possible to control the boat after the wind shift display at 06h30 and 18h30 european time), it can be dangerous to use the scheduler when close to the ground, as you experienced it).
Sometimes, the Auto heading tool or the waypoints can help quite well.
Hope this is clear enough.
Regards