I think making each connection ameliorable to throttling and the the other countermeasures clients typically use is most important, although I don't know enough about networks to be more specific. If it's easier, making every connection error exactly once may give a first idea of possible changes to the results.

A client-specific, randomised error rate would be the second step. Without this, the test is still meaningful. But it measures the system's response to internal failures, not to a typical production environment where most clients see 0 dropped packets, and a small number encounter most of the errors. I'm not sure how dropped packages are distributed, but I would guess 99.9%+ clients have none, yet those that see any might actually get an error rate far higher than 3%.