Wiring 100 Amp subpanel
You have the right size wire, although the aluminum is no harder to work with than the copper

You are calling out the correct gauge wire for a 100A feeder, which is good, and you are also correct that distribution lugs are rated for 75&deg;C wire, allowing you to use that column on the ampacity chart (110.14(C) point (a)(1) even permits it for &lt;100A, never mind point (b) permitting it for 100A and up in any case).  However, your assertion that copper will be smaller diameter/dramatically easier to work with isn't quite right.  Fat aluminum wires are compact stranded by default, as opposed to the typical concentric stranding of a stranded copper wire, which means they do not take up much more space than a copper wire of equivalent ampacity.

There is also no minimum height for a panel

While you cannot have a breaker handle over 2m (6'7") from the floor (to make sure that folks can reach it!), there is no minimum height requirement, and large commercial panels sometimes are 6' tall or more, with breakers starting at 12-18" above the floor.  This means that your plan to put the subpanel below the main panel is fine; do remember to pull the bonding screw out of the subpanel if it's shipped with one fitted, and torque all distribution lugs to their specified torque with a torque wrench or screwdriver that reads in inch-pounds.  (This last requirement is a new one in the 2017 NEC, specified in 110.14(D)).