Can't help on cross dominance, that's a training issue mostly. I'm a righty that's left dominant, but trained myself to shoot right dominant.
As for astigmatism, there are a couple ways you can go on it, but it really depends on how bad the astigmatism is, how well it is corrected, and the type of correction. So long as your rx is recent/current and you don't have a massive cyl adjustment, a huge chunk of the work is already done. Tolerances on glasses are pretty tight, but medical conditions like diabetes or just aging can make pretty notable changes over time. Keeping a script up to date is important for that. Contacts are nowhere near as precise as glasses for cyl and axis adjustments, but they can work decently for a lot of folks. Glasses will always be more precise when compared to mass produced RGP or soft contacts though.
For red dot style optics, either green dot reflex sights like the Holosun 510C-GR, holographic sights like the Eotech or Vortex UH-1, or TFO optics like the Meprolight M21 and Trijicon Reflex are the easiest to work with. Different reasonings as to the how, but all of them have a reduced measured brightness (not perceived) compared to a standard red dot sight. The eye is more sensitive to green, so it takes a lower power output to see a similar brightness compared to a red dot, holographic sights use a diffraction grating that scatters the light into a whole bunch of dimmer dots instead of a point light source, and TFO sights have a mix of low brightness mixed with polarization and dichromic filtering. Eotech does do a green reticle as well that would probably be pretty solid because the mix of green light and holographic diffraction, but I have yet to see one in the wild.
Additionally, you can use a flip up or fixed rear sight as a diopter to further reduce coma/stretching or similar as it'll further reduce the light hitting your eye.
Any optic with an adjustable diopter (scopes or most prismatic sights) will give you a couple diopters of adjustment as well, but it comes at the cost of needing to train yourself to work in the eyebox of the optic.