D1 is in the wrong place (on the circuit diagram at least) - it should be on Q4's drain and then to ground/0V - sort this out, let us know what happens and consider using fewer words to get a better response - I read this a while back and lost the will to survive, entered a coma but recovered a few minutes ago!!
Honestly dude - stick to the business and you'll get better answers (and a bit quicker too).
Trying to get an N channel working can be tricky given the supply bootstrapping required. I think you should try something else first (and this will potentially teach you more about this type of circuit). This would be a natural progression in my book....
At the moment, I think your regulation technique works by pulse skipping i.e. when the output voltage is high enough (despite the diode in the wrong place), you kill pulses on their way to Q3 by shorting its gate with Q2. Instead, try setting up the 555 to have a variable duty cycle (instead of fixed) and avoid pulse skipping - variable duty cycle will give better ripple voltage and I think it's more important than trying to replace the P channel with an N channel - there are plenty of buck regulators using a P channel for Q4. OK maybe Linear tech tend to use N channels on a lot of devices (with bootstrapping) but it's no shame using a P channel and building from scratch.
There are of course, plenty of bucks that do use pulse skipping but better performance is from PWM/duty cycle modulation. If you get that going then try using an N channel FET to replace the flyback diode (D1, the one that appears to be in the wrong place on the circuit). That gives you a synchronous buck converter and better efficiency.
If I've misread your diagram, don't be shy, tell me (in few words but with accuracy).
360 W at 120 V will draw 3 A on full load. (From P = V * I)
Connect with an inline fuse in the L wire and make sure you connect the earth / ground lead.
Any forked or ring terminals that fit that size screw are likely rated for 3 A or more. If all the strands of your mains lead wires fit inside the crimp barrel it's a good sign that all is well.
Best Answer
It will almost certainly be fine to connect one of your hots to the "L" terminal and one to the "N" terminal and set the switch to 220V. What matters is the voltage between the "L" and "N" terminals not where that voltage happens to be in relation to earth.
Note that a 120/240 switch is a sign of an older power supply design that will almost certainly be inefficient and have poor power factor.