Re: Modern Psionics
Are you looking for rules or campaign settings? If it's rules, they can be modified to fit the campaign, if it's a campaign, why are we discussing rules?
You had brushed off Traveller as being too sci-fi, but if that's your only objection, it's easy to drop the future part out. Skills can be substituted or just dropped altogether.
Really though you have to think about what kind of game you want to run and where you want it to go.
If you want a grandiose game where the heroes become larger than life and are unstoppable by normal means once they are quite experienced, D20 would be a good ruleset.
If you are looking for something "more realistic" that regardless of experience a .50 bmg round will still kill or remove limbs, go with a system like Traveller or a modified Shadowrun or similar.
I don't really know where Gurps fits into those two.
Now think of what you want them to do with their psionic powers. Do you want them strictly codified or something looser?
Codified would be more like spells, each power has a set limitation, range, damage, etc. This provides an easier time for determining what can and cannot be accomplished, but leaves little in the way of freedom or variation.
A loose system would be like the have the Telepathic ability, if they want to read someones mind, they have to make a skill or power roll based on the situation. Even a minimalist character can push the limits or do things a bit differently.
Now the setting itself is a whole other ballgame and that might influence the choice in rules. Super hero type games tend to do done better with a codified and leveling system where a gritty, 'realistic' game trends toward the other direction.