A full, all day sun, south facing patio is not a good situation for any Japanese maple, regardless of specific location. First, while some JM's are indeed more sun and heat tolerant than others, ALL would prefer morning sun and then some shade from the intense, hot afternoon sun and many require it. Second, there is an issue of reflected heat from the paved surfaces of the patio. Third, and this was not specifically addressed, if these are going to be grown in containers, all bets are off.

Yes, they'll burn - even in the midwest (lower zone), most JM's in full sun experience scorch. It's even rather common in my very northerly, weak summer sun, zone 8 maritime climate. And coloring will be washed out by very intense sun, turning most red leaved selections a muddy green-bronze color. Will they outgrow it? It depends on the selection, your soil conditions and how much care you provide the plant with regards to watering, etc. but not always.

What you propose is just not preferred siting and places unnecessary stress on the trees. Is there nowhere else on your property these could be located?

No, they will not be container grown. I would like to plant them where I can readily see them and both locations have full, all day sun.