What do you mean by “stricter”? You can crank down the variance in a Dirichlet by cranking up the concentration. @scholz’s suggestion of a multivariate logistic normal lets you also model correlations.
How is theta defined? Why make the prior scale proportional to the value? It means a value of 0.1 gets a prior scale of 0.02, whereas a value of 0.5 gets a prior scale of 0.1 and a value of 0.9 gets a prior scale of 0.18. @jsocolar makes the good point that the prior isn’t multivariate normal here, it’s truncated. The truncation isn’t a problem—Stan will handle that appropriately implicitly. Where truncation becomes a problem is when the data is inconsistent with the truncation and probability mass piles up on the boundary. I don’t think that would happen here, but it’s definitely something to watch out for.
The multivariate logistic has the same benefits as the Dirichlet in that it’s already normalized to the simplex.