Can't be done out of the box by Marketo and honestly, if your "campaign score" isn't the number of successes, it doesn't sound like Marketo should be responsible. Like most good things though, it can be done with a developer, in your case Apex in Salesforce.
What are you intending to score at a campaign level? i.e. write down your criteria
We need to base the scoring on the campaign level, not the contact level so that this score syncs to campaign level as well as the opportunities, is this doable without needing apex?
You're still not clear enough for me to help. What is the scoring at a campaign level that you want?
e.g. Sum person scores for all persons in the campaign?
Count the number of successes in the campaign?
Count the number of opportunities from the campaign?
FYI, the above can't be done by Marketo out of the box