How do I summon a command block as a falling block with commands inside?

You do not have to do any of the work yourself. Just go to a command generator site such as this one by Tschallacka (archive) and enter the commands, one-per-line. It will spit back a command that summons a command block tower and removes itself when completed.

Credit to Fabian Röling for his answer!!

Technical Explanation

Very brief, refer to Fabian's answer for more details and give the guy an upvote for his troubles :)

Any entity can have a Passenger NBT tag. This is an entity that is 'riding' the parent entity. The passenger can be another falling block. However, due to a bug, the passengers of a falling block land inside the block they fall on. This can be worked around by placing an armor stand in between each command block, which will immediately die and separate the next block from the previous.