Lee-Roy, this is a hard question to answer correctly so you may achieve the desired result in your garden.For instance, where and how large will the area be- -are you looking to create an actual orchid meadow ,as you mentioned the possibility of mowing and removing all clippings as one attack plan.What are the orchids that require low fertility that you wish to grow?
"Soil fertility is the ability level of soil to grow and support plant life. Fertile soil contains the sufficient minerals and nutrients needed for plant growth, and it is often composed of large amounts of topsoil."
When you started your garden renovation, the ground sloped from the back towards the house.You then leveled it by creating terraces and that the soil was fundamentally clay.How fertile is the ground now and what is the PH?Is the PH right for the type of orchids you wish to establish?In leveling it off, did you bring a substantial amount of infertile sub-soil to the surface?
I'm not sure that I would attempt a large area to start off with, you also have somewhat limited space, plus 2 dogs.
I haven't done or even considered this type of venture, so take my thoughts for what you think of them.
Over several years, you could do your first scenario, but even though you enjoy the "activity of gardening", perhaps it would be too long, bring disharmony to the household and bring on another "blue-green hosta episode".
If the grassed area being considered is too fertile, I'd remove the sods a spade depth, take them up behind the last shed, stack them upside down and let them rot down for humus to be utilized later elsewhere.Buy in some grit or very course sub soil, incorporate it into that now depleted grass area.
Or, still get a professional soil test done and if OK, plant into the existing grass area.Mow it as you suggested.This way if it is not a raging success, you still have your grassed area and perhaps sanity.
PS I'd be itching to establish that steep sloped area behind the shed into a ''wild garden'' incorporating rhodos and all sorts of shade loving plants and bulbs and all the other stuff that you don't want to admit you actually like.