I don’t know if there are any generic hacks, but coming from similar culture, my points are -
The biggest winning point for Amazon is - Document culture. In fact, pre reads are such an integral part of any level of meetings, all VPs, SVPs take time to read instead of bombarding questions. Not sure, if there’s something missing in your team. If yes, maybe keep sharing those documents before talking to those stakeholders.
Throwing under the bus is again a very common trait I observed at amazon, you have to remove your dependence and be honest if you don’t know something. Asking time is never looked down.
Reading all your inputs make me a guess that your team might not be having a program management support. Many single threaded owners don’t believe in PgM and expect PdMs to handle it. See, if you can ask for a PgM support.
Last but not the least PdMs play a significant role in decision making process, help in aligning the stakeholders. Your communication will build reputation, which is a valuable currency at Amz.