We do this differently, what we do is have at many of our customers locations the LTE Backup always running with the same piority as the wired WAN connection (it could be a secondary WAN connection rather than a LTE backup too). To make thing work, we use outbound policies, piroitising traffic to the required WAN connection, this still leaves the LTE Backup connection accessable.
In many of the Balance & MAX range of routers, we also use a feature for PPPoE modems we run in bridge mode, this allows for the bridged modem to still be accessed for management and support, if this connection is our secondary connection then keeping it active and also using the outbound policies is essential.
Have a go with your out bound polocies, you can create the policies first before changing the piority of your connections if you wish to progrsivly test the changes.
Happy to Help,