Taking another look at this, I would agree with Connorsrpg's suggestion that the process of swapping which stances are "readied" should be during a Short/Long Rest. That lines up better with other classes/archetypes, and fits better within the 5th Edition style. Plus, for some reason I had thought that at 3rd level the Fighter could only use those two, similar to the Battlemaster's maneuvers. I didn't realize they could choose from the full list, and their level determined how many they could have "ready to use" at any given time. That's a bit more powerful, so yeah I'd set the reset period to an official "rest". It's a bit more elegant, and it would be easier for both players and DM's to keep track of during gameplay. Along those lines, I would consider limiting it so that they didn't know all 6 stances/strikes right at 3rd level. Perhaps something like this:
Level 3: has learned 4 stances, can ready 2 at a time
Level 7: has learned 5 stances, can ready 3 at a time
Level 10: has learned all 6 stances, can ready 4 at a time
or something similar? And maybe even at Level 15 or 18, add the ability for him to have all 6 stances readied all the time.
I'm also not so sure about the mechanics behind expending and recovering the uses of strikes, it feels a little awkward. Simply using one bonus action to recover all expended strikes seems a bit unbalanced, especially at higher levels. If you want to limit their use, then I would suggest requiring the fighter do something for each strike in order to "reset", or giving them a certain number of strikes per Short/Long Rest, possibly tied to either fighter level or an ability modifier(perhaps Constitution, suggesting the physical toll they take on the fighter, so that those with more endurance can perform more of them between rests).
Another possibility to consider, rather than reducing the fighter's ability when it comes to stances at the early levels, delay the introduction of strikes until Level 7 or 10, keep their number of uses limited, and possibly buff their power to compensate. That way you treat the strikes as a more advanced form of Legion training beyond just the stances.
I'm not sure how optimal any of those ideas might be, but those are what came to me as I took a closer look at things. Still not sure how to work the Eagle spirit into it all, but I definitely think it should be something that is featured at multiple levels, not just at Level 7.
On a side note, have you ever read the Codex Alera book series by Jim Butcher? It's a six-book fantasy series(it's already complete, so you'd have none of the angst all the Song Of Ice & Fire fans are dealing with), that took as one of its points of inspiration the legend of the Ninth Roman Legion that mysteriously vanished from history(you have to finish the series to find out just how deep that influence goes, but it's a neat little twist). Reading this thread has made me want to go back and read those books again.
Haven't read the books and I was seeking out for a new series to start (Finished Simon Scarrows excellent eagle series for the 3rd time now). Thanks for the suggestion.
Look, I believe both systems can work. Legionary only brings 2 stances to a fight at level 3, battlemaster brings with 3 maneuvers (to be used with 4 superiority dice). Legionary can change his stance before or after encounters, which is how I imagine them - they have to play smart, be prepared.
The readied maneuvers, recovery and stances&strikes are mechanics from 3.5's Tome of Battle. If it works there, it can work here too.
I'll be playing a game with a friend just to test the legionary in a week or so. I like how it is right now, I don't want this to replace the battlemaster with their x times/short rest gameplay. I want it to be more spammy, suitable for longer fights, with an expected DPR a lot less than the battlemaster.
The original design introduced strikes at level 10. However, I decided that introducing a whole 2-3 paragraphs of feature after level 3 could be more trouble than it helps. That's why I ended up combining the strikes with stances to reach the position they are in right now.
TL;DR : I'll test it. If not broken don't fix. If broken, short rest tactics.