Let's say my hypothetical Monk is using Tiger Claws to deal double his Unarmed Strike damage as a full round action.
Elemental/Stunning Fist(s) don't seem to have an action associated with them that I can find. So would it be possible to just say "I use one of my Stunning/Elemental (or both?) Fist attempts with this"?
Yes. Stunning Fist (and similar feats) modify an attack you make, regardless of when or how you make it.
Benefit: You must declare that you are using this feat before you make your attack roll (thus, a failed attack roll ruins the attempt). Stunning Fist forces a foe damaged by your unarmed attack to make a Fortitude saving throw (DC 10 + 1/2 your character level + your Wis modifier), in addition to dealing damage normally. A defender who fails this saving throw is stunned for 1 round (until just before your next turn). A stunned character drops everything held, can't take actions, loses any Dexterity bonus to AC, and takes a –2 penalty to AC. You may attempt a stunning attack once per day for every four levels you have attained (but see Special), and no more than once per round. Constructs, oozes, plants, undead, incorporeal creatures, and creatures immune to critical hits cannot be stunned.
Special: A monk receives Stunning Fist as a bonus feat at 1st level, even if he does not meet the prerequisites. A monk may attempt a stunning attack a number of times per day equal to his monk level, plus one more time per day for every four levels he has in classes other than monk.
Yes, Stunning Fist and Elemental Fist don't use their own action, so you can tack them on to any unarmed attack. And Tiger Claws is still an unarmed attack.