My immediate thought is to create a new class that overrides the framework's padding. I'd need to look at the dependent styles first, but thinking as I type, I would do:

<div class="grid-x grid-padding-x padding-half">
...
</div>

I would then create an overriding style in your scss stylesheet with the following:

.grid-padding-x.padding-half {

	padding-left: map-get($grid-padding-gutters, medium) / 2;
	padding-right: map-get($grid-padding-gutters, medium) / 2;

	@include breakpoint (small only) {

		padding-left: map-get($grid-padding-gutters, small) / 2;
		padding-right: map-get($grid-padding-gutters, small) / 2;

	}

}

This is assuming you are using SCSS first, and then compiling your css from that. If the override is conflicting, stick an !important in there as a last resort. Try being more specific with your selectors first though.

Hope this helps!

Thanks, I'll give something like that a try. Although I would assume the padding would need to go in cell descendants as well.