I don’t think there is a much better approach than treating them as hyper-parameters, at least not in this generality. In particular you won’t get around having some other metric of “was this a good pick”. You’re not required to vary them randomly, using intuition also works many times.
When you get to specific losses that have specific interpretations, things may improve (e.g. there might be probabilistic interpretatons or you in very specific cases it may be useful to try to achieve similar orders of magnitude in the loss contributions).
Best regards
Thomas