In general sharp blades should work better with coarse hair, particularly in a mild razor. I say "in general" because the razor can also be a factor. Even a Derby Extra can give me a decent shave in a shavette.
Maybe get a Maggard slant head to help hack through the undergrowth? If you do try a more aggressive razor start off with a very light touch and experiment - carefully! - to find the best head angle.
You could also try going against the grain at an angle instead of direct. The more you knock down the stubble the easier it gets. To stick with 3 passes, try the 2nd pass at a slight angle (if you can) and then the 3rd at a steeper angle. That might get you there.
The right razor head, with the right blade, and the right touch will give you a great shave once you find them.
Maybe get a Maggard slant head to help hack through the undergrowth? If you do try a more aggressive razor start off with a very light touch and experiment - carefully! - to find the best head angle.
You could also try going against the grain at an angle instead of direct. The more you knock down the stubble the easier it gets. To stick with 3 passes, try the 2nd pass at a slight angle (if you can) and then the 3rd at a steeper angle. That might get you there.
The right razor head, with the right blade, and the right touch will give you a great shave once you find them.