Actually, SK is a rather easy target for NK. A few years ago, the brief was 4-6 days, even without using Slime.
US defense and reinforcement plan, without Nuc, is non-operational. US forces there are simply a tripwire.
Kim’s problem is not taking SK. It’s what to do with it once he did, so he never will. He wants nucs and delivery system so world will give him more bribes not to fire them, as US did for decades.
I think Kim might get into Seoul, but that’s about it. The momentum peters out after that. He has no fuel reserves and an army he probably canot resupply.
One analysis I read 15-years ago suggested he might try to seize a chunk of SK territory in the mountainous area to the East of Seoul and hold it as a bargaining chip. Might be possible, but what would he trade it for?