Psst: internal dashboard to track the number of stamps which non-paying users used this month won't take you five minutes to implement. It is a single SQL query, right? I know you'll have to discard a working Excel system to do it but from the moment you're done to the moment you die you will never have to update that Excel file again. Process efficiency! You can crank out as many of these little micro-things as you want and put them in a single dashboard, which will give you a quick health check at a glance, minimize time spent bookkeeping, and make you not waste too much time digging into reports when you could be working. OK, tangent over.
There is nothing wrong with giving people free things that actually cost money, as long as your COCA (cost of customer acquisition) is substantially lower than your LTV (lifetime customer value). It is no different, conceptually speaking, from doing something like paying from AdWords for a user who might convert into the trial but never into a paying user. I'll probably pay Google close to $1,000 this month for that: this is safe because I have historical data and a failsafe (discussed later).
It has also been my experience that most users go up-or-out very quickly on my service. If that continues to be true for you, you have very little to worry about.
If you speak to an accountant, who are generally conservative types, they will recommend you to do something to cap your maximum liability via this. For example, you can clarify that unused free stamps expire at the end of the month. (That might already be the policy. If so, smart.) You could also reserve the right to yank that offer at any time. I'm not a lawyer, but I think that is likely to be as simple as merely yanking the offer at any time.
I'd put a failsafe in the system to prevent you from spending over $X on free stamps in a day, for reasons similar to why Google only has authorization to charge me $X in a day: if the process goes suddenly out of control, have a human think things through before saying "Oh, sure, 1500% growth is totally normal under these circumstances. Spending approved!" It might happen because you ended up featured on the front page of the NYT. Congratulations. It also might happen because you ended up on 4Chan when some enterprising individual suggests using your service to send a million pictures of genitalia to some public figure who has made statements they do not approve of.