I think you may be on to something when you consider that torque may be an issue. Although the 12:1 gearbox works great, you are turning a very large traction wheel. Good for going fast, but not so great for pushing or turning.
You might want to try changing the gearing in your tranny to get the 16:1 reduction for more torque.
Another possible problem would lie in your code... perhaps it is not producing a sufficient differential between the left and right gearboxes in order to force them to turn.
There is absolutely nothing wrong with having traction wheels in the front and omnis in the back. We've got it on our robot and it works fine.
Check it out. We have a very similar layout to yours (front wheels are 6" traction wheels driven by two CIMs through the 12:1 kop transmission then geared up a bit with the sprokets for speed) and two 6" omnis freewheeling in the rear. The key difference is that with two CIMs, and the smaller wheels on our robot we have roughly twice the torque reaching each wheel. That makes a HUGE difference.
When designing a two-wheel drive robot it is also important that you put as much weight over the drive wheels as possible so that they do not slip. If your weight is over your undriven wheels you will have a problem. You should also use the conveyor belt as intended, with the sticky side in contact with the carpet to ensure maximum traction from your driven wheels.
So... boost your torque... the best bet if you can do it (it will be a challenge with weight) is the 2 CIM adaptor for your current gearbox. The next best bet is changing your gear ratio, or reducing the diameter of your wheels (can you try 6" traction wheels?). Also check your weight distribution and see if you can move some of it over your drive wheels.
But there is nothing wrong with having your drive wheels in front and omnis on the back.
Good luck,
Jason
Okay, that link shows our robot picking up a ball... but the other videos on that page show us driving in practice and we're also on the Blue Alliance if you want to see it work "for real".