This would be very tough...though I do love my puh-sychic powers.
I thnk, to do this properly, just off the top of my head and throwin' stuff out there, let's start with this...
First and foremost: CHANGE THE NAME! "Psionics=Psychic Bionics"..not very fantasy-ey. They are decidedly and admittedly (if I'm not mistaken) a "sci-fi" element thrown in as an option back when Swords n' Sorcery, Pulp and Sci-Fi were not necessarily all that different...it was all "fantasy."
Just call 'em what they are: "Psychic Powers" or something else simple and straight forward...even just the name of the power themselves...You're not "psionic" you're "telepathic" or what have you.
On the note of powers, WIPE THE BOARD CLEAN! Forget all of the "psionic" stuff that came before.
Telepathy and Telekinesis. Those are essentially the basis upon which any/all other "psychic abilities" stem from or are contained within.
Start with those. Make those work.
Read people's minds. Speak to them wordlessly. Form telepathic rapports/bonds with your companions. Empathy. Psychometry (picking up/sensing residual psychic energies in a particular location). Astral Projection. "Hold Person" via telepathic induced paralysis. "Telepathic Invisibility and Illusions" (by altering what the subject thinks they see), a "Psychic Scream/Area Attack or Bolts." Suggestion. Domination. Mass suggestion and domination. Protecting yourself and others from "mental" spells and magical effects (fear, charms, confusion, detecting illusions, etc.)
Move things with your mind. Light things. More heavy things. "Gross" control (throwing the table in the tavern across the room or busting open a lock/door) verse "Fine" control (untying your rope bindings or adjusting the tumblers to open a lock). "Stop" things (like arrows, then boulders) coming at you (and "fire" them back!). Telekinetic concussive force blasts/"push" effects. "Hold" effects. Levitation and eventual flight for yourself and others. "Force field" shields and/or domes/areas of protection from physical and energy effects.
Basically old style "psionic/psychic combat" (the Tower of Iron Will and all of that) is just all "telepathic combat" (color it for/as taking place on the astral or ethereal plane if you like). Need to work out a system for that as well (psychic v. psychic battle of wills type stuff).
Sounds like plenty for a Psychic/Psion character to play around with to get started in the new game.
Then worry about "psychoportation" <rolls eyes> and "cellular adjustment"/whatever it was that "innate shapeshifting powers", "Soulblades" <eyes roll OUT of the head>, and whatever else has come down the "Psionic pipline" through the years get bundled in some other "expansion/psychic hero supplement" later.
--SD