In NAT-mode the AP itself is default gateway for the clients. The outgoing packets are NAT-ed by the AP using its own management IP address, so naturally in its VLAN too.
Probably not very good practice, but you could put the management IP of your access points into a VLAN that is in an isolated environment with the cheap broadband gateway therefore having the guests traffic going out that way.
The corporate Wi-Fi users would get put on another VLAN that goes to the Meraki Firewall via a bridge mode SSID that has VLAN-tagging enabled.
@HodyCrouch 's solution above is another possibility. But then you need to provide DHCP on that guest VLAN using either your DHCP server or the Meraki MX.