Instead of a monthly subscription, anyone can use the site but advance functions require credits/micropayments. For example, Basecamp - if you add more people its $2 per month per person. if you like to add 50mb or 100mb add $2 or $4 month. Would this work? This has happened in the MMO space. whats stopping it from working in the web app space?
I believe it works for banks as well. They keep taking small fees for almost anything you do, and the fees are just a bit too low for customers to really care.
I believe the best way would be that you write these prices into the agreement up front so you are allowed to charge the fees whenever they do stuff without really informing them. It is though important that the fees are really small so the users do not care. What if Financial Times said that there is a fee of 5 cents for each loading of the front page and 10 cents per article? That would be fine by be as long as I did not have to get my credit card each time.
I also do not consider 2 or 4$ microtransations. Amazon EC2 for example charges 10 cents for each hour you rent a computer. 10 cents is below my "radar" so I do not consider it an expense and often let it run for a few days without caring.