OK, good point. I don’t think it will be possible to move (transition) the tunnel but it depends on exactly what tunneling protocol is being used. So you would have to accept that the old tunnel will fail (if the interface has gone down) and create a new tunnel (on the other interface).
Maybe you need to hook into the interface up/down script (discussed elsewhere in this forum) - so that when an interface comes up / goes down, you ensure that there is a tunnel over the best available interface.
To protect yourself while that is happening, you may want to use the firewall permanently to prevent any other traffic going direct to the internet.
Generally speaking, an event driven approach is preferred to a polling approach (i.e. not cron).