Here is my suggestion.
Use the paladin class, less Spells and Lay on Hands.
In their place, boost up the mount. Allow a celestial or fiendish mount (the "neutral" Crusader could choose either?), and be sure to use full benefits of it being a Magical Beast (give it d10 and feats and skills as a magical beast).
This kind of forces the neutrals to lean towards good or evil, but clerics need to do that already anyway with spontaneous cure/inflict and turn undead, so maybe it's not so bad.
Change Smite Evil to Smite Infidel:
If LG can smite any evil or CN.
If LN can smite good or evil (choose at character generation - it must line up with turn undead and mount choice) and CN.
If LE can smite any good and CN.
You might also consider allowing an additional smite every 4 levels or so, to amek up for no spells.
There. This is the simplest way I could think of to get where you want to go.
Another possibility is to set up a new class, sort of. Make them start as a fighter and switch to a prestige class (of your choice, not theirs) at a certain level - the pre-defined path pretty much makes it a new class. You could even type this up as a new class - while it would look a bit odd, it would follow the rules pretty well and, presumably, already be balanced for you..