When I ordered the new front sensor for my '02 3.4 4WD, I'd ordered one with a flange mount, as the original. The new one came as a spark plug type screw in with compression gasket and a flange adapter.

When I screw the adapter onto it, it uses up about 3/16" of the sensor probe. I cleared the codes and started the engine and all seemed well. Car runs, code lights stay off, but when I drive it I get a very fast surging, like a shuddering and the car has no power at all - can barely hold speed limit on highway.

A check with forums online showed me one person with the identical problem, which he solved by unplugging the sensor. Lights came back on, but surging/fluttering problem was gone. I tried it and it worked for me, too.

The replacement they sent has the same setup. I have the tools and the skills to cut the ridge off the adapter and cut the threads on sensor to match and let it go about 1/8" deeper. Do you think that would solve the problem ?? Is it possible the new sensor is defective ??

I made a 3 part picture in Paint to show it all, but can't seem to drag and drop.

You didn't post what brand sensor you went with. The front sensor is so important as it reports back to the ecm on trying to keep the best air fuel ratio. And how quickly the o2 sensor reacts has an affect on drivability.
Since the important role that part plays, I hope you got an OEM or Denso for a o2 replacement. Anything other than those brands is problems that you don't need.

I can understand why you want to go aftermarket on the 2001-2002 oxygen sensors. Reason why the OEM ones are so pricey is because they are not oxygen sensors but Toyota's version of a air/fuel ratio sensor, except that it works on a 0-1V scale instead of the much more common 0-5V scale. This is the one you want: 403 Forbidden. You can try searching on places like Amazon for cheaper but avoid buying from irreputable 3rd party sellers. You can buy it direct from DENSO for $131.

Pulling the sensor out of the exhaust stream or adding a spacer will cause the sensor to run lean.