Can Marketo prevent individual prospects from receiving more than 1 email per week?

I'm not totally clear on why communication limits wouldn't work for you. From what you described, that's exactly what the built-in limits are designed to do.

I believe you can't apply Comms Limit dynamically to individual records.

Before Comms Limit was available, I had set something up to prevent my nurture campaigns to be sent if the lead had already received another email. It wasn't pretty but it did the job! It had: 

1. A "Daily Email Count" custom field 
2. A trigger campaign that added 1 to Daily Email Count every time an email was sent (Email is sent, Email is any)
3. A campaign scheduled to run daily that reset Daily Email Count to zero
4. Nurture campaigns (this was before Engagement Programs) that checked that Daily Email Count was zero prior to sending an email

This may be over simplifying things, but maybe you could set Marketing Suspended = TRUE when an email is sent to the prospects that fit your criteria, wait one week, then set it back to FALSE?

In addition to what Nadia says: we used to have a Smart List called Overmailed. The List's condition was like:
Was sent email = email is any
+ constraints:

# of times: 2
period of time: This Week

Then just exclude members of Smart List = Overmailed in our e-mailing campaigns (no matter engagement or other)