Stormguard Warrior

What is the best way to qualify for this feat without actually taking levels in a class that grants initiator levels?

I know the Martial Maneuver/Stance feats. So I guess a more specific question is: what would be the best maneuvers and stances (and thus at what levels should you take x class) to get via those feats, and the best classes to do it with? Assume a character who wants to use Robliar's Gambit and the like. Generally Fighter-ey or Knight-ey.

Don't forget to save on one feat by picking up an Iron Heart Vest for 3k gp. Totally worth it, unless your DM is the type to take away characters' equipment frequently.

Wall of Blades and Iron Heart Surge are two of the best Iron Heart maneuvers, and they're both low-level.

Besides those two, you need a stance. Punishing Stance and Absolute Steel are the only two low-level options you have. Both of them are decent but not great. (Well, Punishing Stance is pretty devastating at very low level play, but it doesn't scale, so it ends up being "just ok.")

So: at about Level 6, buy a Novice Iron Heart Vest that will let you learn Wall of Blades. About Level 10 take Martial Study (Iron Heart Surge). Somewhere in between there, take Martial Stance (either option) and Ironheart Aura. Then when you've done all that, take Stormguard Warrior ASAP.

Note that Stormguard Warrior really gets a lot scarier when combined with TWF.