Low cost frame synchronized (genlocked) 3D stereo camera
You probably will not achieve a 100% perfect result with your setup. That you got them synced to a 1FPS accuracy is pretty amazing actually.

Professional stereo setups use frame locking in hardware to ensure the cameras record in perfect sync.
This is not possible with ordinary webcams. If you fix the recorded video in post you can get to less than 1/RecordingFPS'th of a second accuracy which can be enough depending on your framerate. The higher your framerate the smaller the offset will be.

If the webcams offer some sort of low level api you might be able to improve the results even further but I doubt thats available, thats usually something you only get in (rather expensive) industrial cameras.

Edit: Regarding your edit, Genlocking is the way to go with pretty much any video application if you need 100% sync (or as close as possible to that, you will always have some nano/microsecond delay between frames).

Being it syncing videos displayed on a display wall (all these individual displays need to show the correct portion of the frame at the same time). Or recording with multiple cameras the same frame at the same time.
Resolution isn't a factor here.

Though price definitely is. Do you have a budget for this project or is this for hobby purposes? There are definitely (non-cinema) cameras that would support this though they are not exactly cheap as a webcam.
The cheapest solution I can think of is using the GoPro Stereo Rig. http://gopro.com/camera-accessories/dual-hero-system
This would put you at a budget of 1000$ in total (minus a few cents). Not exactly cheap but definitely affordable.

And the GoPro is also a very flexible solution. You can shoot from 3840x2160@15FPS to 848x480@240FPS. It also supports raw HDMI output which can be helpful if color precision is desirable or live monitoring of your shoot.

A downside is that the GoPro has a fish-eye lens. You can reduce the distortion by setting the camera viewing mode to narrow and using this nifty software hack but you wont get fully rid of it unless you replace the lens.

Edit 2: If you go the "build your own electronics route" you should have a look at the ArduCam project. It's essentially a shield for the popular Arduino boards. It allows you to connect several cmos modules like the OV5642 which is a 5MP sensor that is also used in the Raspberry Pi camera module.

According to this thread on the RaspberryPi forum these modules support genlocking.
While its not possible with the pins broken out on the PiCam module (though there are some ideas about how to do genlocking with it on the last page) you can order these modules cheap (25$) from ebay and use them with the ArduCam board. Even if you don't connect the modules to the same oscillator to do genlocking you should get some pretty good results as you work pretty close metal here also the Arduino plattform is very easy to use.

With such a setup you could potentially make a 1080p stereo 3D rig for around 125$.
50$ for the cmosm modules, ~16$ for 2 Arduino Uno clones and 60$ for 2 ArduCam shields.