Ha we are on a similar boat, if not the same. I'll share some ideas:
I'm playing with a script that goes into the mailbox and searches for specific contact emails avoiding unrelated stuff. Then displays the email subjects and it will allow me to reply using an specific email address per site/account.
One email address doesn't do the job (I believe), because it's a network of sites and if someone writes to best-widgets.com they expect email answers from there, not from any other email address from other domain.
Many emails require standard "thank you" answer, I will develop several variations that can-could be used randomly, nobody wants to get the feeling they are talking to a machine. Besides, it will be me, not automatic replies. I mean, most of 100 emails can use templates, adding-modding only the important unique parts.
I'm married with Perl so I'm playing with that code right now.
each client be assigned a unique email address, ie: email@example.com contacts support and our reply is sent as fred-blogs-site-com@mySite.com so that we know instantly which user is trying to poison the well.
Ticket software already have options so you can deal with emails and classify them, both via contact form and via email mailbox.
I'm not going that way because of personal preference, I hate setting up extra software using X databases making difficult or at least time consuming to move from server to server in case of migration. I'm also caught in the "DIY" I find many pros there.
About that unique email address, you could pick the first message and assign an ID, then use that ID on an email perhaps on the subject like "RE: contact info [ID#42517]" (mmm I don't like it because people might edit it and you are lost then) or you can use the same ID ON the email like "RE: whatever" but from firstname.lastname@example.org. Easy setting up a catch all option on your server. That way they could reply to contact-WHATEVER@site.com