Extra clock savings: don't touch the DB at all during the exams. Dump the validated submissions as single field delimited strings to a flat file or NoSQL or similar.

Excellent tip. You could use a key/value store like DB_File to save each submission. If you can construct the form "action" attribute to give it a unique path (perhaps using Javascript on the client side) then you would not even have to parse the query arguments:

<form action="myapp/user1/question1">
<form action="myapp/user1/question2">
<form action="myapp/user2/question1">
[download]

Then use $ENV{'PATH_INFO'} as the key ('/user1/question1'), and read from STDIN directly to get the raw value to store.