Specific feats I'm looking for are Endurance and Iron Will, since I figure those would be the most likely, or Psionic Meditation, Psionic Weapon, or Unlocked Talent. All but Unlocked Talent are required for PrC class entry so I can't have them on a weapon or anything. I hope to gain all 5 of these feats before level 5 and I am getting one bonus combat or teamwork feat as is. The reason for the Unlocked Talent feat is to meet a manifesting a specific power requirement so that does not need to be actually on my feat list but expanding on that is grounds for another question.
If your game uses the anti-hero optional rule for the hero points optional rule system you can gain a non-class, non-race, non-level-derived bonus feat. This is the only way to gain an intrinsic bonus feat without spending class or race resources on it.
If you are a half-elf or can pretend to be one Paragon Surge, by far the best spell in the game before the nerf-bat hit it, can get you another 'feat for which you meet the prerequisites' which is effectively a bonus feat. It only lasts 1 minute/level so it's not too useful to you.
You can get tons of feats from ioun stones, which would let you qualify for class entry, but you stated that you aren't interested in equipment based solutions so we wont go into detail on that.