I like the idea of new classes, or at least modified classes. I have been intending to customize the classes as well. I would love to see your take on the specializations you mentioned.
I don't know if standard DnD has this, but in Pathfinder every class has a number of "archetypes" that modify the standard class template. They're different from prestige classes because they're not a separate class. They just modify an existing class. For example, I made a monk character recently using the Zen Archer archetype. It modified the basic monk template by allowing the use of arrows instead of unarmed strikes for the flurry of blows ability, changing the list of allowed bonus feats, and swapping out some of the usual monk abilities for a few cool archery tricks.
Some of the existing Fighter archetypes are archer, brawler, corsair, crossbowman, dragoon, gladiator, mobile fighter, phalanx soldier, polearm master, shielded fighter, tactician, two-handed fighter, and two-weapon warrior. I imagine some of these could be adapted to Codex Martialis without too much trouble, or you could create your own. The polearm master gets a special ability at level 2 called "pole fighting" that's essentially a half-staff ability (allows you to shorten the grip to use against adjacent targets) in place of the usual Bravery ability. At level 17, they replace Weapon Training with a new ability called Step Aside that lets them take a 5-foot step back whenever a creature moves adjacent to them.
However, if it's "feat bloat" that you're worried about, you might want to consider creating feat packages that people can choose on top of any other abilities they get. So everyone would get at least a few of the basic MFs needed for whatever they want to specialize in.