Excellent idea! If you make them convincing enough it will eat up a lot of man-hours of processing time as well as postage (if they are indeed prepaid). I wouldn't write the Second Amendment or anything else so obvious on them since these will be quickly thrown away.
Are there other places to obtain these forms than from police departments?
Keep in mind that it MAY be a violation of law to provide false information on these forms and send them in. But this is what civil disobedience is all about. Just take some precautions. Don't let it be known that you've grabbed a whole bunch of these forms. Also, you may want to send them from towns you don't live in. Remember that handwriting is like a fingerprint. Speaking of that, I'd suggest wearing gloves when handling them.
Yes, maybe it's paranoid, but they may want to make an example.