Expand your horizon, trade it for anything better on any day of the month (unless you need a specific day off). Do that for every garbage trip and eventually the puzzle will start to unlock.

Obviously the more specific days off you 'need' and the higher the length of the trips reduces the solvable permutations. Turning both of the 4 days into 3 days is what I would try first but I don't want long trips. If you do then just try to make it a less onerous 4 day that starts on any other day. Load it all up for every trip you want to improve and wait for a batch run, then check immediately after the run for a real-time trade. Rinse and repeat.