On the other hand, since I’m familiar with sheet-mulching & Hugelkultur, would it be best for long-term soil health & stability if I dug 12” down, put a weed barrier, then a layer of pebbles for drainage, then a layer of branches/small logs of apple & maple wood, then some old leaves and compost, then dump 6-12” of mixed soil on top, then some mulch?
Sheet mulching is a great way too.
"If" I dug down 12 inches, I would skip the weed barrier and pebbles. The " layer of branches/small logs of apple & maple wood, then some old leaves and compost" would give it the natural drainage I would need, then I would put back the soil I dug out. As it makes no sense to haul it away to be replaced with imported soil. Then I would add some form of mulch, wood chips, leaves, any plant material etc.... whatever I could get my hands on.
Now digging down 12 inches is a lot of work so you have to determine if the plants that you want to grow really need all that effort. Carrots yes, they would be very happy to have the depth, but most perennials have strong enough roots to root down if they need to and usually their roots grow on the top layers of the soil as feeder roots. Now if I did dig down, then I would likely want to have large quantities of logs & branches to make my effort justified if I had access to that material. On the other hand, those who do the double dig method, just simply loosening up the clay soils has worked wonders for a lifetime of thriving plants so one does not neccessay "need" logs & branches buried to have thriving plants. And garden beds where I did no dig but simply piled on the layers of "mulch", the plants thrived too. So if you have the energy and time, digging down in the soil has benefits.
If I have a garden bed area that is not urgent to plant in that season, I will pile layers of plant material & leaves, small branches to prepare the harden soil for the coming season. The mulch layer will keep the clay soil workable and moist when it is time to plant.
Note: the reason I don't recommend a weed barrier as what does that weed barrier look like in a few years when all the roots are tangled in it. Most weed barriers do not decay and are forever stuck in your soil tangled in roots. I have seen it, and done it and have learnt the hard way. This is not what nature intended. Learning about permaculture as steered me away from this technic. Adding a layer of pebbles 12 inches deep has no advantages. If your soil is high in moisture then plant the kind that likes moisture or raise your bed 6 inches or so or on higher mounts to get above the water table for those plants that like less moisture. Pebbles, either you go to the river bed to find them or you buy them. I cannot see myself doing either unless I really wanted to create a very small decorative rock garden for fun.