On the peer flapping, in all likelyhood you are losing the IPSEC tunnel causing the flap. So check for the reason that the tunnel is not stable in the logs. On routing, this requires more thought on the needs. Why do your resources in AWS need a default route? Are you providing internet access for your AWS resources via your PA firewall? If not, then you likely do not need a default up this tunnel. Instead just advertise the resources on your network that the AWS resources need to access. If you do need the default route to AWS, your peer should be eBGP and when it does re-advertise your local default route it would re-write the next hop to be itself, your side of the AWS peering. Thus the traffic would come to your AWS peer from the AWS resources.
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