I think you need to consider exactly what you're defining here. I think you can do this, but your society will be problematic, and you'd have to embrace that.
There are three aspects. You want a
- redeemable reward that is
- allocated based on merit
- as evaluated according to contribution to society
Let's consider two out of three.
1 & 2 = Capitalism
Yeah, yeah, capitalism isn't perfectly merit-based, but whatever. Roughly, what your talking about is one party evaluating someone else's contributions to private ends and rewarding accordingly.
#3 would have to be pasted on by a central authority that redistributes based on corrections for private versus social returns. But most capitalist economies do some amount of this: funding scholars and teachers and police, taxing corporations.
1 & 3 Aristocracy, Caste System, etc.
If you have redeemable rewards based on contributions to society, than your society has a strong rankings of tasks according to how much each contributes. Those who function in this system do receive some sort of pay, i.e. redeemable reward, but it is often rigidly set by norms and typically one's place is assigned by heredity.
#2 must be pasted on, and how it is done depends on what you mean by merit. If it is overall merit at some central task, you assign caste or status based performance at this task, and status determines reward. This is similar to Lilliput (as in the case of a non-sense taks) or traditional Chinese bureaucracy, as in the case of a centralized exam. If you mean merit within a task, then you create room for rank, and cash wages are based on that.
2 & 3 Utopias
I think this is what you mean, and it really gets at the heart of what is described in Utopias such as Doctorow's Down and Out in the Magic Kingdom and Edward Bellamy's Looking Backward. You see, if you picture yourself rejecting cash because that's not the idea you mean, then what you are rejecting is the full redeemability of the reward. That is what defines cash. Anything that essentially differs from cash is somehow not fully redeemable. Doctorow has Whuffie, which is not fully redeemable because you do not deplete it, but rather use it to queue up for scarce resources. Bellamy has a fully equalized ration of goods that does not depend on work, but more difficult or perilous work is compensated by shorter hours, i.e. excess leisure, which is not fully redeemable.
The trick here is not thinking about how to paste on #1, but thinking about how to handicap #1 in such a way that the reward you speak of is not effectively cash. There must be things that money cannot buy that the reward can buy, unless you strictly forbid money altogether. Someone must decide what is valued; this can be a central government, but not necessarily. Maybe society as a whole has a long-lasting tradition of valuing some castes more than others, and castes have elders who recognize extraordinary individuals within the caste?
I hope that's an interesting framework.