Hey, Christine, even your last resort option doesn't actually quite get it done because you can't write to the standard SFDC "Campaign First Associated Date".
Here's the Idea to change that (from two years ago!):
https://success.salesforce.com/ideaView?id=08730000000hqOCAAY
Meanwhile, the work-around is to create your own date field (and a workflow rule to mimic the functionality) - and then you can upload your own data retroactively to this new custom field.
Another option is to switch reports to "Lead Create Date" to the extent that filling out a form is largely associated with a new lead creation too (depending on how many repeat fillsouts you have).
No easy options here
🙂