How to open multiple PDF files at once?
To answer my own question: while I haven't found a completely satisfactory solution to this problem, I have discovered in Adobe's Reader app the "Recents" list - which shows recently read documents in the descending order of last-opened date. This, combined with the fact that the Reader app remembers the position of each document that you read, and the fact that the "Recents" menu is only a click of the back button away, gives a workable solution to reading multiple documents at a time, albeit slowly.

I wish that someone from 1998 could come back in time and give us proper multitasking. How great it would be!

For now, I hope this idea helps someone else.