...maybe there is an easier way to meet my goals of never messing up exposure.
Exposure is important but by no means the only issue in photography.
Depending on one's subject matter either depth of field (mediated by aperture and focus distance) or freezing (or even blurring) the action (mediated by shutter speed) are crucial considerations.
So while all the factors that you have mentioned certainly affect final exposure it is not a matter of indifference as to which are altered for final exposure.
When I am shooting landscapes from a tripod I work out what aperture I want first (generally an aperture that encompasses the scene as far as depth fo field is concerned), then set my ISO to 100. Shutter speed is anything that just prevent the highlights from blowing.
The order of events here is not random because I am doing everything I can do maximize image quality for the circumstance.
When I am shooting wildlife and birds with supertelephoto lenses then shutter speed is the absolute priority.
Usually a shutter speed at least twice the reciprocal of the focal length is required for sharp images (image stabilization notwithstanding).
In this case the aperture will most likely be wide open and the ISO pumped up to whatever level is required to get a good exposure.
Shooting handheld is different again and it can become increasingly difficult to marry all the elements together that are required for a high quality image especially in lower light situations.
So, exposure, per se, while an important element of image quality, needs to be achieved in concert with the lowest possible ISO (to minimize noise) and a shutter speed fast enough to prevent camera blur. Note that the end-point that I am seeking is good image quality not just an exposure end-point
Maybe you are completely astride all these issues, in which case I apologise for boring you silly, but perhaps something I have written is useful to you.