First of all, have you checked if the cell tower that you're trying to connect to support the frequency of B1, B3 and B7?
The modem chooses to connect to other bands if it's impossible to lock on the ones you defined in Band lock, but if it hooks up on the band - it stays there as it supposed to, at least that is what I've tested right now and it works.
Could you please clarify if you're able to band lock with other devices and the same operator? Have in mind that if your phone or any other LTE device has a higher LTE category - it might connect easier as it has better overall connectivity and signal.
Also, you could try maybe resetting your router to make sure there's nothing else that may be set in your config files that could have an impact on the band lock. It's not very likely the issue, but worth a try.