Stopping Human Spam Through Contact Form 7

I have recently taken over replying and handling emails for the shop and have noticed a lot of spam emails coming through Contact Form 7. I have installed Contact Form 7 Honeypot and also have Akismet installed and configured. The only thing I have not done is install a Captcha which the owner’s don’t want to do. I am still receiving spam email through the contact form, but it is coming via humans submitting their spam, phishing and advertising directly. I get about five to 10 a day and it is really annoying since there is so much other email to deal with.

Is there a way to set up a filter to detect certain words, strings, etc. to stop human spam from coming through, but not prevent our customers from contacting us?

The page I need help with: [log in to see the link]