I've been contemplating this from the opposite end as I am just starting out with Spark. I've been digging deep and the reality is, as others have suggested, that everything between the Laravel side and the Vue side is strongly related - of course!
I have gone from being okay with Laravel from about 3 years ago, to being pretty comfortable with Spark in a few weeks, while also learning a lot of other stuff at the same time.
I think it's really worth investing the time to learn about how Spark works and why; the Vue 2 course here on Laracasts will get you to close to where you need to be, I am up to episode 31, but found myself more than capable of understanding a significant amount of everything in Spark from a few episodes earlier and being able to implement my own components and hook them into the Laravel side. If you work through the examples there, then go and look at the code I think you will be very pleasantly surprised.
If you then look for all the files related to billing it should become clear how you may add additional billing methods. As I say I haven't done this yet, but my initial investigations didn't make me run away in horror. It's actually very clean.
Yes, there will be confusing moments and hours of frustration along the way, but if you already have an application built in Spark I can only see a huge rewards for your time and effort.
I will check in occasionally and do what I can to help if you decide to go ahead and keep posting your findings here. Feel free to tag me so I get a notification.
When you get there you will see how good Spark really is!