Fixed order of same-score query results

At our client we are running several site instances with embedded repositories. On one particular page, we perform a query where we simply get all items of a certain type, sorted by date (descending). What we are observing now is that the order of the returned hits is random, if these hits have the same date (and the same JCR score)! For example, on server 1 the order of the results could be:

document A
document B
..

while on server 2 the order is :

document B
document A
..

To solve it, we could add a second ordering to the query on some random field, for example the UUID of the document. This would force the same ordering on every server. BUT, this involves quite some work, because we'd have to change a lot of queries to add this 'fallback' / secondary ordering. Can we solve this in an integral way , e.g. in the repository ?