We have planted bunchberry, Cornus canadensis, along with the native Trillium, Trillium ovatum and pink fawn lily, Erythronium revolutum under our largest Japanese maple. They provide a spring show before the maple leafs out. Smilacena stellata has also run into this bed and takes over once the fawn lilies and trillium are done.
Cyclamen hederifolium, C. coum, C. pseudibericum, and snowdrops seem to do well under the small leaved maples also. A small leaved ivy might work if it could be kept within bounds. Nice group of Erythroniums in Silver Creek's photo, wish they would spread as well here.
You might try a dwarf bamboo. The challenge here would be to choose the size, color and vigor of the bamboo so that it thrives but doesn't compete too aggressively with the maple.
Pseudosasa owatarii is the smallest -- barely topping 6 inches here in New England, though in gentler climes it is said to be capable of reaching 18" or so. Pleioblastus viridistriatus is a bright, yellow-green variegated cultivar that remains less than 12" tall for me, and is also available in an all-yellow form. Sasaella masamuniana 'Albo-striata' is of about the same stature, has lovely variable cream stripes in most of the leaves, and tolerates dry soil better than the others, in my experience. Both of the latter look especially striking in contrast to red or purple-leaved cultivars.
I've never tried Pleioblastus shibuyanus ‘Tsuboi’ but it's a beautiful little plant and perhaps a less agressive spreader.
All these are running types that will spread by rhizomes, but I've never found them to be a problem and they're easy enough to contain or to yank right out if they grow where you don't want them. You could plant them just outside the maple's root zone, and let the natural spreading habit of the plant take over from there.
Fallen maple leaves among still-green bamboo is a beautiful sight in autumn.
In spring, for the sake of tidiness, many people cut the bamboo right down to the ground to make way for fresh new growth. I seldom bother with this.
I have been growing many different types of perennials under all my Japanese maples (except the weeping cutleaf maples) for many years. These includes primroses, dicentra, corydalis, hosta, helleborus, heuchera, aqualigia, anemone (dwarf varieties that flower and disappear in spring), Japanese painted fern, and polygonatum etc. Some of them may not be overly happy under there but do reasonably well. I have to ripe out over crowding vinca under one of them every couple of years. However, your soil condition is likely a significant contributing factor as you have suspected. Another factor could be you prefer to leave your maple full and thick, and the shading is very heavy under the maple. I prefer to thin out my maple trees to have a more airy look.