So let me see if I get this right......
You can do an excellent floor line "bhs-layout step out" on just about any surface imaginable..... spring floor, rod floor, tumble track, vault runway, fold out mat, and 4 inch landing pad. You can keep your rhythm and alignment on most if not all of these surfaces, and keep your arms straight, get a decent and straight push from your hands to transition into the layout and move strait and centered into the layout.......
So did I get that right?
If I got it right, I'll tell you what I think may be going on. You want this skill, and just don't quite see yourself as being either capable or ready, and it doesn't matter which because if either is true you're going to make the same mistake. So what's the mistake?
It just may be that you're feeling you have to do your best possible bhs to have a chance to make it through to the layout well enough to at least land safely, but hopefully to stick it as well. So how should you do your best bhs?..... by trying harder.... or having faith in the bhs you've done easily for a very long time. My vote would be to do the same bhs you've done for the past year, because that's what you're used to. It's the basis for the timing, core tension, hand push energy, and step-out alignment that all happen before you set for the layout.
These small parts of the bhs must be done correctly to feel comfortable as you set and commit to the layout, just ask your coach, and then ask your coach if he/she feels a deep level of responsibility to limit your new skills to those you can do within a reasonable level of safety and success. I'm sure you already know the answer, but ask it anyway because it never hurts to hear those answers straight from the coach's mouth.
So you might be wondering why you shouldn't try harder. Well, things change when you try harder, unless you're already trying harder all of the time...... which really helps to make gymnastics easier...... and if you are trying harder all of the time there's no way you can put any more effort into the skill. That means, in a very real sense, that trying harder is going to cause something to change, like more arch tension, faster arms and hands, earlier or wider step-out, or slightly turning your hips to get the first foot down (too early of course).
So here's the deal..... Do not change a single thing. Do not try harder. Concentrate on your rhythm, timing tension, and alignment..... or just relax and let your body do what it remembers from the thousands of back handsprings you've let it do in the past, because it's "been there and done that".
Respect your body, respect your coach, and respect yourself.