I think the main problem with the knights is that you're meant to keep everything that you gained from the previous order, they also gained extra proficiencies, it's why the rose knights required so much experience to advance. Surprisingly the dragonlance monstrous compendium better explains how they are meant to work. It calls them a variant of paladins with a few changes.
- Crown knights have weapon specialisation and specifically calls out that they gain no special abilities of the paladin.
- Sword knights gain all of the special paladin abilities and spells.
- Rose knights don't say they gain anything explicitly (other than more proficiencies) but it is implied they have all of the paladin special abilities. I'd give them the sword knight spells as well, even though the books state that the sword knights are the clerical order.
Something that always struck me as weird was that the heads of the wizard orders we level 17 for red and black and level 18 for white so two of them had no access to 9th level spells. Makes more sense in the context of 1e where the orders gain spells sooner.
It's still one of my favourite settings, but yeah, you would definitely have to work on the knights a bit to make them work better.