This doesn’t pass the red face test IMO. The hyperscaler networks are indeed very expensive, but that’s because they need to provide non-blocking or near non-blocking performance within the availability zone, and the clouds don’t charge for this service.

The Internet egress part ought to be straightforward on top of this: plug as much bandwidth worth of connections into the aforementioned extremely fancy internal network. Configure routes accordingly.

It’s worth noting that the big clouds will sell you private links to your own facilities, and they charge for these links (which makes sense), but then they charge you for the traffic you send from inside the cloud to these links, which is absurd since they don’t charge for comparable traffic from inside the cloud to other systems in the same AZ.