I'll throw this out there since no one else has mentioned it, by "3-way" do you mean one half is switched and one half is always powered? If so, any standard outlet can be adapted to that arrangement. Just break away the little tabs on the side to isolate the upper and lower outlets.
I agree with others that the correct fix for short wires is to add "pigtail" wires to the short wires with a wire nut, then connect the pigtail to the outlet. Assuming you have enough room in the box, of course.
As for the push connection, I would be surprised if they are even allowed by code anymore. I have personally seen several outlets with burned connectors due to loose connections. They basically rely on spring tension to maintain the connection and the springs often get weak over time. Dangerous fire hazard, I wouldn't use them even if they're allowed.
What you can do is buy a higher quality outlet that has clamping style connectors. They're essentially like a standard outlet, except you insert the wire under the clamp and tighten the screw, instead of wrapping the wire around the screw. They will easily handle a 12 gauge wire.