There are several factors at play here.
Astigmatism correction is, as has been mentioned above, both a combination of the power of the cylinder, and the axis. In theory, once you get an astigmatic correction in your lens, you should be set. However, there are some exceptions to think about:
1. Astigmatism is a bulge in the conea. Sometimes this bulge can change, based on the pressure you exert on the soft tissue surrounding the eye. So when you form a cheek weld, your astigmatism could change from what the doctor measured, and indeed might even change between positions. I expect this is not common, but I know at least one shooter who has this issue.
2. Lenses work properly when you look through the center of the lens, and more importantly, when you look perpendicular through the lens. When you start to look diagonally through a lens, you create an astigmatic error. So in shooting with regular street glasses, especially in prone position, you aim while looking through the extreme upper inside corner of your lens, and you are looking at almost a 45 degree angle through the lens. The amount of error you get here depends on how strong your lens is to start with, so not everyone has this issue, but it could be a factor.
All scopes have adjustable eye pieces that allow you to adjust sphere power, I have yet to see a scope that adjusts cylinder power. But to answer your original question: yes, I have made cylinder corrected lenses for people that they glue into a lens cap for their scope, so they add cylinder correction to their scope. That would do several things for you. First is it would present the lens perpendicular to your line of sight, regardless of shooting position, it would also allow you to swap between powers, and finally, it would let you manually tune your axis, as you can rotate the lens cap. This last thing is a 2-edged sword, as eyepieces usually rotate to tune sphere, which will rotate your axis, so getting the focus set up is a little tricky to twist the eyepiece while holding the lens cap stationary. Good news is that if you paint a line on the lens cap skirt, you will know where it goes and can get it back tot he same spot.
I don't recommend trying to go with 1/8 step lenses, both because they are difficult to source, but also I do not think they are necessary. If you want to play, I'd suggest your prescribed cylinder, and then get two more of +0.25 and -0.25 shperes - though even there - I'd start with the right one first. It could be that just mounting it on the scope solves your problem.
I make lenses for $40 that are AR coated. If you order, I need to know the scope diameter, and I can cut the lens. I can't help with the lens cap, it would be up to you to see how it is mounted.
Two more quick things. First: Hydration level and blood sugar level (actually glucose level inthe ocular fluid) will drive the focal length of your eyes, so stay hydrated, and eat through the day if you are shooting a match.
Also, focus your scope by screwing the ocular all the way out to start, then screw it in while looking through it, and stop as soon as it comes into focus. THis is the point that your eye is doing the least work. I used to screw it to find max/min positions, and try and go half way between. THis is wrong. You want the eyepiece screwed as far out as possible when shooting.
Art