That line about buyers being tired of handing over email for a PDF they skim in five minutes hits hard, because if they skim it in five minutes the sales team is calling a name that was never really a lead.

What's the actual gap at the mouth measure? If it's a quarter inch or more, the iron is never going to get proper support no matter how flat the sole is, and that's your chatter right there. Did you check whether the frog sits square to the sole, or if the iron itself is flat? A lot of those no-name planes have irons that are dished or bent, and no amount of lapping fixes a bad iron. Also worth asking: is the chip breaker mating up tight with the iron? A gap there lets shavings jam under it and you get exactly the crumbled cereal you described. If the iron and chip breaker are fine but the mouth is huge, you could glue in a patch of hardwood or brass to close it up, but honestly on a $25 plane with a warped sole you're polishing a rock at that point.