Lens optics/geometry question

I have astigmatism in both eyes. It isn't that bad looking across the room at black letters, but a block away from traffic lights, it's stark. For my left eye, one light looks like three - one slightly "smeared", two of them basically crisp circles. Always arranged in the same specific triangle pattern. For my right eye, it's close to the same, though no "smeared" circle, one of them is kinda dimmer than the other two.

For whatever reason, sitting in the chair hasn't gotten me a good prescription yet for my left eye - four failures in a row over the course of two years from a couple different optometrists. I gave up and just wear the glasses and suffer through it.

My latest prescription is fine for my right eye. It's not 100% perfect, but it's really quite good. For my left eye, it's not as bad as without glasses, but there are still three dots, just arranged a bit differently than without glasses - the light is closer to a single dot but not quite.

However, I CAN twist the left lens in a way that makes the image pretty clear. I'll use aeronautical terminology to describe what I mean:

I "pitch" the glasses down approx 20-30 degrees. I then "roll" the glasses counter-clockwise (from my perspective) about 40 degrees. I "yaw" them slightly to the left, maybe 5 degrees - not terribly important, and I feel like I can generally get fairly clear image with just the pitch and roll parts. I do take some care to get the focus to be through the same spot on the glasses and I try to keep the distance from my eye to the lens as close to normal as possible (tricky with frames, but I'm aware that this probably matters).

My question: Given lens spherical diopter, cylindrical diopter and axis, as well as the pitch/roll/yaw angles, can I determine equivalend parameters that would result in a lens that would give the same refraction? I can imagine this being a "no" if the change in refraction depends on more than just the prescription - e.g. maybe grinding geometry, materials, etc vary from lens to lens, etc, and different lenses.

My hope: IF there's an easy answer to the above, I'll diligently estimate the pitch/roll/yaw stuff, do whatever math, figure out a hopefully better prescription, and order a pair for under $10 and cross my fingers. If they work well, I'll go shell out real money for a nicer pair.

My level of understanding: I know how diopters work, sph and cyl, and I get cyl axis. Given those three, I know basically how parallel beams orthogonal to the lens are focused and how that focus varies depending on their alignment with respect to cylindrical axis, etc. (maybe botching terminology a bit, tho) My background is mathematics, so I understand the the pure geometry aspects of this decently. I'm no optometrics, nor am I a physicist, optics, engineer, etc, so I DO understand where my understanding ends. All that to say, if you have an affirmative answer but it's just equations with lots of trig and calc, I'm all ears (eyes?) - I'll put in legwork to figure out WTF you're telling me. But if there's no good answer or it's too hard to convey, I get it. ANY help/advice is appreciated.

Thanks!