Keep the existing TGW-based architecture and introduce an intermediate C8Kv router that peers via eBGP with your vMX and with eBGP over GRE with the TGW
Transition the customer to CloudWAN tunnel-less connect, which does not require GRE encapsulation in BGP. Think of Cloud WAN as a natively multi-region TGW construct, similar to vWAN Hubs in Azure.
Untested: It may be possible to use the MX19 BGP in IPsec capability to peer a vMX to a TGW, as TGWs also support IPsec encapsulation, but we have not tested this use case.