Looking at the variant, and I have a couple questions.
1. What casting stat is used? I assume it's wisdom, since all of the Swordsage's other abilities are based on it, including Maneuver DCs.
2. Can you learn Maneuvers and Spells, or just spells? If it's the latter, how do you handle stances?
3. How do you handle metamagic? I assume it'd be handled like a Sorcerer, but I'm not sure.
4. Assuming caster level is handled similarly to initiator level, Arcane Swordsage 7/Abjurant Champion 5/Fighter 1/Eldritch Knight 7 would give 18 BAB and 19 CL at level 20. Holy shit. (OK, this isn't a question, but still, holy shit.)