Photos of crevice gardens show flat stones laid on edge to form roughly parallel lines. But how are the lines supposed to be oriented, so it looks more natural?
Our garden area is on a slope. Are the lines supposed to follow the contour of the hill, so they are horizontal? Or are they supposed to run from high to low?
Well, speaking only for myself, I can only throw out my opinion which is that there is no defined "right" way! ;-) Where strata resembling "crevice beds" occur In nature, the orientation of the slabs is in response to geological factors. That is, the slabby nature is often, though not always, due to the existence of original horizontal bedding planes in the sediment that formed the rock - planes of weakness along the different layers that were originally laid down flat. But the overall orientation of the slabs we see now is often due to much larger events. In the Rockies in this area, it is largely due to thrust-faulting, where the collision of plates during mountain building pushed large blocks of strata over one another in an easterly direction - the result being that older strata often override blocks of younger strata. Anyway, all this large-scale earth movement meant that blocks of bedded rock could end up tilted at various angles - anywhere from almost horizontal to vertical to completely overturned. And let's say we're seeing this on a ridge of exposed bedrock in the mountains - that originally-horizontal bedding could end up being perpendicular to the long axis of the ridge it's on, or parallel to the ridge, or anything in between. So, really, with respect to what is "natural", anything goes! (And I suppose it is fair to point out that most rock garden beds don't look anything like "natural" anyway - they are very artificial constructs in the majority of settings, but so long as they grow alpines well, I guess they are doing what they're supposed to! :-) )
In the garden though, considerations may be different, and here is a practical one: Having the lines run parallel to the long axis of the bed (i.e. horizontally, or at an angle from horizontal) would be easier to manage for erosion, so that top dressing is not washed down slope in heavy rains. Given that you describe your garden as being on a slope already, this may be quite important.
Probably best to peruse lots of photos of crevice beds and see what appeals most to your eye, given the shape and size of the bed you're planning and the type of rock you'll be using.
Here are a few links where you may be able to get some more ideas, or get more opinions (as at the first link, the Scottish Rock Garden Society):