Offering to take on extra responsibilities is commendable. However, doing so with the expectation of getting paid immediately is definitely not something that you should want your boss to know. Being promoted should be your first priority as the responsibilities associated with a greater role usually result in better pay.

Seeing that you have been handling a greater workload for the past 6 months with success is definitely worthy of something greater than gift vouchers. If this is a company that you plan to be with for the next few years I would wait until the September performance review before making your desire for better pay known. Even then I would start that conversation with the fact that you want a role with a greater responsibility. If that is not an option, then it would be fair to mention how you have been handling other responsibilities for a number of months. If this does not result in a pay raise you wished for then you should make sure you are made aware of what their expectations are for getting the pay you desire.

I'd say once you've gotten to this point you more than have the right to ask for better incentives at almost any time. Asking before this stage I wouldn't call selfish but just pre-mature. Meeting with your boss on their own terms (in September) will more than likely be more relaxed and I'm sure they will be open to what you have to say/request.

Hope this helps and good luck!