I would not put the vent inside the wall. There are a number of reasons for this:
- An exterior wall with just 2x4 studs should have that space full of insulation. Trying to put the vent inside the wall will either compress the insulation or require removing some of the insulation. In both cases the loss of insulating capability is not good.
- Trying to install this inside the wall requires opening up the wall and then re-patching.
- Vents like this capture a certain amount of lint dust over time and they need to be taken apart and cleaned. I use one and have to clean it every couple of years. The lint gathers because the sharp turns in the air flow cause the lint to fall out of the air currents.
- Dryers only last a certain number of years and have to be replaced. If you customize for your current dryer by burying the adjustable vent in the wall cavity you will no doubt be having to re-open the wall at the time a new dryer comes along.
The chance of saving much more space when using a periscope type vent is unlikely. Like I said before I have one behind my dryer and it is very difficult to reach behind the dryer to tighten the clamps on the dryer and pipe that sticks out of the wall. If the space behind the dryer was any less than the minimal amount required for a periscope vent it would not be possible to get to the clamps.