If I were to create my own custom banishing ritual (and fully intent it to work), would it be just as effective as well known rituals like the LBRP? If not, then what makes those rituals better? From what I’ve known the intention to banish is all that matters.
I’m thinking of making a ritual that’s a combination of the Sword Banishing and LBRP. I’d start with the sword banishing (without the angels) and then draw the pentagrams while charging them with my own divine power.
I would say it would be more effective. The reason for this is you are refining a method that works perfectly for you, with your energy and your mindset, to most efficiently and convincingly draw on your will to perform the operation.
As long as you manage to create within you the feeling of banishment it shall work.
You just need to understand the idea of banishment : sending away an unwanted force/spirit.
Think of each word of that sentence and try to picture what inner pictures comes to you.
To me, banishment feels like fire that goes up and destroy any sticky feeling attached to me or my room/house.
After things burned down, it remains ashes. So i would use air/wind/brooms to cleanse the ashes away.
Then i will need to re consecreate me/my room/the object with a new intent (I am perfectly cleared). Then shielding it.
This logic comes to Jason Miller 
All ritual should be custom
Would it be more effective? I’d say: it depends on the ritual! If you involve Gods or spirits that have the power to cleanse, or make sense in the context of the ritual (Gods or spirits presiding over the directions, etc.), then you may find it works better. Or, when it comes to using items, like creating purifying water, you may find that ingredients like sea salt (Considered purifying because of its holiness, and virtue of washing away) or bay leaves (Traditionally considered purifying) may work better than swamp water (But I can think of some contexts in which the swamp water might be able to draw all impure things to itself). Or, using swear words (Possibly having power to avert evil because of its “obscene” effect) may be more effective than saying something like “Sir Johnanthan the Fourth!”.
Experiment and see what happens! When it comes to banishing evil spirits or influences, well, unless you have evil spirits and influences around you constantly it would be hard to pick up on whether something is effective or not, but with general cleansing I think you can pick up on what is more effective easier with time.