psionic shot and greater psionic shot will not work as they are explicitly called out as damage (type: psionic) much in the same way that some sources of damage are pure arcane energy or diving energy, the psionic 'x' feats all deal out pure psionic damage.
Where did you find that it's Psionic damage? It just says it adds damage to the Ranged Weapon attack so, since the damage is not specified, the damage should be of the same type of the attack (similar to how the enchantment bonuses on weapons or sneak attack dices deal the same kind of damage that the base attack does).
Anyway even if it's psionic damage it would still work, since the wording of Healing Blast states that it heals by the same amount that the Eldritch Blast would normally do as damage. Even if it's psionic, it's still damage.
The only issue I see is if the added damage is considered coming from another source instead of enhancing the base attack, but while it doesn't seems to be the case to me, I must admit it's debatable...
well, i was certain it was called out, but now that i am searching, i'm finding very little. i found this:
Mental Resistance [General]
Your mind is armored against mental intrusion.
Prerequisite
Base Will save bonus +2.
Benefit
Against psionic attacks that do not employ an energy type to deal damage you gain damage reduction 3/-. In addition, when you are hit with ability damage (but not ability drain or ability burn damage) from a psionic attack, you take 3 points less than you would normally take.
The benefit of this feat applies only to psionic powers and psi-like abilities. This is an exception to the psionics-magic transparency rule.
Special
You cannot take or use this feat if you have the ability to use powers (if you have a power point reserve or psi-like abilities).
the bold text implies that the damage is either type-less, or at least not standard energy. and eldritch blast does eldritch damage, or arcane damage, iirc. so if the psionic x feat is untyped damage, then it would presumably stack. though a tough dm might rule that since the eldritch blast has a type, the only things that increase that specific type of damage would work.
oh well, i'll keep poking around, if i find it, i'll let you know.