It's just that everyone seems to be trying hard to use an ablative absolute. But that's difficult here because there isn't an obvious intransitive verb "to sink" in Latin (this is something I've learned from this thread so thanks) and there is no passive present participle in Latin. So why not just take the easy route?
By the way, the English idiom is "the rats desert the sinking ship" - I don't know why the original poster wants them to jump off.
Nobody's mentioned the single most fitting active expression for this process: pessum īre. So something like Dē nāvī pessum itūrā mūrēs prōsiliunt (I don't like dēsiliunt here, sounds too much like 'casually jump down, dismount'). Or use a cum-clause for a more measured presentation.