There are still quite a few things missing from your clarifications, and still a few things to clarify.
1) You've said in a reply to someone in this thread that casting Techniques is the same action as the class feature and that if an action isn't specified for the class feature (the case for many constant techniques) it should be assumed to be a standard action. You need to include that in the actual Polymath class description somewhere very clear to readers in the Techniques heading. Otherwise, they aren't going to have any idea.
2) You still haven't clearly stated how often a Polymath learns techniques, OR how many they actually know. You have a vague sentence at the end of the section that says they "generally know how to cast one technique per technique slot." This tells me nothing. I can infer that you might mean that they only know a single technique per level, but I don't know if that's true. Is it? Because if so that's probably pretty bad.
3) Time to get tricky. As far as this class is concerned Soul Binding (Binder) is a class feature, as are Inspiration and Arcane Dilettante (Factotum). As far as I can tell you could prepare those as Constant Techniques and get a whole lot of bang for your buck.
4) Another tricky one. You say that the class is able to learn spells and mysteries as Techniques so what about Tome of Battle maneuvers? And if you can learn them are they constant or usage Techniques? I would advise treating them as constant Techniques, usable once per encounter (as long as the duration of the Technique lasts), with no recovery. Stances could work similarly.
Finally, it's good that you went the way of the Technique system, rather than casting class features as though they were spells. As spells you could metamagic class features which could get really messy with some metamagics, and especially with Turn Undead and Divine Metamagic...