Board partners have yet to release the H370 and B360 motherboards at the time of posting this. Your chip would work in a Z370 motherboard just fine and to say they're "not good" is completely false. Some people will buy an overclockable board and chip but never overclock. So, it would stand to reason that buying a locked chip for a Z series board is fine.
In fact, Z series boards often come with more bells and whistles over their H and B series counter-parts. You could get more I/O like USB 3.1 or more RGB options (if that's your thing) and the boards just look better, in my opinion. And one last thing is that you could sell off your 8400 for an 8600k or 8700k and boost your performance from there without the need to change your board...