If you want to meet you criteria (PC 1080p60 3D and sub3000$ projection), then the only current solution is dual-projectors.
I haven't been following projectors recently so I do non know the current models input lag, but since dual-projection is based on the projectors 2D modes, you should have less lag issues.
The good news is that home dual-projectors is no longer stuck with the polarized system since the availability of the Omega system, some types of projectors work better than others due to the colour spectrum approach used by Omega. See the Ultimate 3D projection thread in the >3000$ section and the Omega Optical thread in the 3D tech talk section.
The bad news is that there are still no Hdmi/DVI-DualLink/DisplayPort splitters supporting 1080p60 3D so you need to use dual-outputs. So there are restrictions on graphics cards able to run a dual-projectors with proper sync. At the moment the only card which I know it works are AMD cards with the DDD 3D drivers (Nvidia 3D Vision drivers do not support dual-projectors)