Electronic – What do phase dots on an inductor mean

You don't have to use coupled inductors in a SEPIC configuration. The main advantage is that you can get by with lower inductance windings. If the two inductors are closely coupled, the ripple current is divided between them and the required inductance is halved. So if you want to replace a coupled inductor which has two 3.3 uH windings, you would need two individual inductors of 6.6 uH each at the same current rating.

How did you calculate those inductance and/or timing values? Also, 100 ohms will make that gate switch at a glacial rate. 62nC (datasheet) is a lot of gate charge.

Anyway, if we assume you've got 50% duty cycle and allow current to increase (let's assume the best case, starting from zero) linearly from 0 for 1msec the current at the end of the time (through the 4.7uH inductor) will be 787A.

You need to drive that gate hard with a gate driver to at least 5V and certainly not with the ~150-200 ohms (counting the AVR output resistance) you are driving it with, and to increase the switching frequency and/or the inductor values.

You are getting the MOSFET spending all its time in the linear region at high frequencies and the inductors saturating at low frequencies and the MOSFET not really fully turned on ever (excepting that 5V test).

If you can beg or borrow (I wouldn't recommend steal) an oscilloscope and observe the voltage and current waveforms you will be able to make rapid progress. If not, look at the simulations including current waveforms and put actual values like that 100+ ohms in series with the drive.