This is possible - you just have to think differently.
The VPLS network itself has to be connected to the Internet - and you need to stop thinking of it as an internal private network. Plugin any kind of NAT router to the ONT, and then the VPLS network will plug directly into this. This device does nothing else but provide Internet access. If you like, you could use an MX here, but not it will not carry internal traffic.
The VPLS network will no longer use your internal IP addressing (although it will use some kind of RFC1918 addressing) or connect to your internal network.
Now you are your own ISP, and the VPLS network "is" the Internet at each site.
Now you can plug an MX in at each site, just like how you would plug the MX into the Internet. You can use the AutoVPN over MPLS design guide.
https://documentation.meraki.com/MX/Site-to-site_VPN/Configuring_Site-to-site_VPN_over_MPLS
If you want, you can layer in additional Internet connectivity (including cellular) to provide either back up or primary Internet access. You can also add an additional MX at each site, either plugged into VPLS or only plugged into a dedicated Internet circuit (in which case, it will only be used for failover).
Switching would be like it is now, internal and plugged in behind each MX.
Note that you will probably find it will be cheaper to buy an Internet tail at each site. If this is the case, it will be much easier to simply do this, and then cut over to an AutoVPN based network running off the MXs, and then decommission the VPLS network.