Something is triggering the current limit, the on time is way to short, it should be around 2.2usec when in continues mode with a bit of load on it, according to scope pictures it is not much longer than 0.5usec at 30ohm load,this load is also approximately where this converter should go into continuous mode.
When the output voltage is below target, then it is only a over current situation that can turnoff the switch. (Or reach of max duty cycle)
It is clearly stated in the data sheet, that in continued over current situations the controller will do frequency fold back, ,typical to belov 100khz, this corresponds with you scope pictures.
Your coil might not be saturating, But some thing is triggering the over current protection - could be noise, since you have build it on a protoboard, your ground might not be good enough and causing spikes to trigger over current protection.
According to datasheet your output capacitor should be close to 47uf when having a output voltage bigger than approximately 12volt or a load step could trigger an over current situation.
So try to improve the current paths, add wire or cobber foil, and reduce the output capacitor back to 100uf or less, and maybe use a Rset of 4k7, smaller than this doesn't make sense according to the data sheet.
Regarding to your diode both should work, sb1100 is a bit small with 1A current rating but this is not the reason for The behaviour we see here.
At work I have a similar converter running at 370khz with a 5A schotky without any issues
16 to 24 volt in, 12v out at Max 4A controller is LM22677 very similar to lm2679
Hope you get it is to behave soon
