I can understand your desire to focus on cleanup and not prevention! When I trim my beard I use a large round plastic bucket with a rope handle that completely covers not only the sink but a few inches (5 cm) on either side, and I still find hairs in the sink afterwards which must be cleaned up.
It sounds like the solutions you have tried involve getting the hairs out of the sink and surrounding areas. My solution is just the opposite - I simply wash the hairs down the drain. They are very short and not long enough to stick together and clog up the drain, and it is much quicker and cleaner than trying to keep them out of the drain. If you have a lot of hair in the sink you might be more reluctant about using this method, but it does work quite well if it's only a little hair.