I have done almost all of these thingsI also currently building sepic converter for input voltage 8.5v(minimum uc3843 supply) to 24v and output to 2.5v to 24v. Mosfet FDP036N10A (100 V, 214 A, 3.6 mΩ). I'm expecting to get 150 watt output and 10A max current. At 12v input, I'm testing 12v 6A load by halogen lamp, Input current show 8.5A (efficiency about 70%). But inductor and R sense get hot. I have trying to rewinding different inductor with different core color (yellow-white, green-blue and blue), size and turns. But all have same issue. So i think that sepic converter is not suitable for such high power application.
I have noticed about 4 switch buck boost non inverting converter for higher power, with single inductor. But circuit is seem so complex and i hate that.
I also meet same issue like yours, when output get drop. Try to increasing R sense > 0.05ohm, increase input bulk capacitor above 2200uf or adding one npn transistor at pin 4 to pin 3 as loop compensation.
For reference, see https://danyk.cz/univ_m_en.html
Maybe it will help.
I read the post you mentioned very carefullyBack in post #110 I asked for a scope trace of the voltage across the current sense resistor.