You might be making this more complicated than it needs to be.
On the whole, angels won’t be around unless you call them, and then you can ask the to go away and they respect that, especially if the relationship is on good terms. I’ve not called angels myself more than a hundred times, but the license to depart has never been an issue, they seem to have plenty other things to do.
In this case why not just back off calling angels before it becomes too much? Is it like a switch or do you sense it coming on?
It’s also my opinion that some so called “demons” are angel and deity level beings anyway. So why would “hokey” banishings work on them but not other beings of he same ilk?
In the case that you have been attacked by another mage, via an angel such as Gabriel for justice, the same banishings (that don’t call on the beings you’re trying to banish to do the banishing, obvs.) will work for any entity.
For a more heavy handed banishing for angels E.A. Koetting’s Book of Azazel has a description of doing this using tablets with the deals on them, that are broken as part of the ritual of the Lake of Fire.
I think the best technique will depend on whether you are attacking on thier space or defending your own territory. If I’m being attacked, it’s a straight up fight and I will try to kill, which has the effect of banishing higher entities from my reality. If I’m attacking, I would just attempt to go around them, bind and failing that maybe try E.A.'s technique mentioned above.