Basically, I like for overland travel to matter. I don't like skipping over a two-week journey. Skipping the journey makes the world seem less real, seem two-dimensional, only a painted backdrop.
I have to disagree that "You travel for two weeks, until..." makes the world seem less real than a two week journey involving a dozen or more random encounters, which would be the typical result of your 5 checks/day plus follow-up checks. I guess though it depends on what a 'random ecounter' is here - on one extreme it could be a dozen wandering monsters who all attack the PCs, on the other hand it could be mostly weather, terrain obstacles, exotic phenomena, friendly or neutral NPCs, game animals, and such, with very few monster attacks.
I definitely don't think that "You meet a Manticore, roll init" every day of a two-week journey adds to the versimilitude of a world, quite the reverse. For realism, the fewer random monster attacks the better. The kind of thing which does help a feeling of realism is exotic local colour - a sky island glimpsed at sunset; a migration of furred snakes across the PC's path. And a sense of place - describing the dark mountain range that looms to the north. The stillness of the pine forest. The sunlight glimmering on the lake. Just brief, hopefully evocative descriptions of the world around the PCs.