Running

Loads of things could be contributing to your suplination. Shoes too wide could make your foot move around in the shoe but not suplinate specifically. A shoe too narrow especially in the toe box will likely destabilise the foot as they will bunch the toes together allowing the foot to roll more if you can spread your toes that will help keep your foot flatter for longer therefore suplinating less. Lower stack height will also reduce foot roll. Shoes like the new top end Nikes are very tall with no support and won't help or likely accentuate any foot roll. If you heel strike your foot will also follow a larger arc to toe off so that won't help. Shoes with a lower drop can help you land more mid/fore foot this should also help by reducing the length of that arc. Custom orthotics will probably help but most gait problems originate from an in balance/weakness somewhere. Does your slight suplination cause you injury or just annoying with the shoe moving around? I tried loads of different shoes to try and correct my pronation but every pair seemed to get rid of one problem and create another unit i had a proper gait analysis and bio mechanical assessment by an expert. Turns out i had really strong quads for driving from all the cycling and lazy glutes which are needed for driving but also stabilising this allowed my femur to collapse inward slightly then my knee,tibia, ankle then foot = my pronation and resulting in problems with my foot and hip. Loads of stretching, strengthening and glute activation work now i can run all day injury free in any shoe as long as it fits. I know every runner is different and my problem is different to yours but any shoe even orthotic will simply act as a crutch and won't actually fix anything. Your problem is probably with your body and not your shoes so fix that ideally. All the running strength and conditioning actually improved my cycling too as it made me much stronger and more solid as the core work and stretching helped hold a good tt position for longer and the glute work really helped with long climbs as you have a couple of large muscles to recruit i can ride on the rivet for max quad power then shift back on the saddle and use a bit more glute and hamstring keep alternating and hold climbing power for much longer some riders switch between climbing out of the saddle and spinning which is the same principle. But it costs money takes months of work and most of it is a boring but now I'm so glad i did it. Otherwise maybe try some altra escalantes and see how you get on