Shade and potting soil sound OK.
Deeper pots are definitely better. Shallow pots just dry out way too fast in drier climates.
Water running out the bottom of a pot is NOT an indication it is well watered. Dry soil shrinks so the first place the water runs is down the sides and out the drain hole. Water runs out the drain holes well before the soil is properly wet.
If the soil is a little dry it may become hydrophobic and actually repel the water.
One alternative is to soak the pots in a tub once a week. That helps to make sure the entire root zone is properly wet at least occasionally.
I use repeat watering to make sure the water soaks in properly - water as normal then come back a couple of minutes later and water again. First water slowly soaks in maybe 1/2 inch max while remainder runs away. Second water rapidly soaks into the damp area and then penetrates another 1/2" or so. A third repeat may be needed to get water right to the centre of the pot. I believe this is probably the reason for the Japanese saying to water 3 times - once for the leaves, once for the branches and once for the trunk.
Another alternative is less water over an extended time. My trees do well with automatic watering as the sprays operate for 10-15 minutes which is way longer than anyone will stand and water the pots and gives the water time to penetrate right through.
Trees that have been in the pots for several years also dry out quicker than recently potted ones. Roots must constantly grow so gradually the spaces in the pot fill with roots, leaving less and less space for water as time goes on. I've found it better to repot some trees with fast growing root systems each year or it becomes difficult to get them through the summer. Maples generally take a few years to reach this point though. Young trees that are growing well get root bound far quicker than older, established trees so allow for both species and age when deciding how often to root prune and repot.
What really puzzles me is the red swamp maple. I collect them from the roadside in absolute full sun. The ones out there in nature don't seem to show signs of stress. Maybe bigger, deeper pots?? Higher percentage of organic soil components??
Remember that roadside trees have the entire earth to hold water for them and roots can go far in search of enough water to keep them hydrated. Your potted trees have very limited space for water so will run out so much quicker.