I would suggest that in addition to increasing the size of the contact area of the feet, you also need to change the overall shape of the mech as well.
Given issues like the square/cube law and stability due to the centre of gravity, a mech won't scale up like some monster human, but rather will become wider, have "tree trunk" legs that are proportionally much wider than human legs and likely a relatively squat torso. The idea of "arms" is really a bit of a non starter as well, the changes to balance while moving multi ton arms around (much less the recoil of arm mounted weapons) would make moving and fighting immensely more complicated.
If anything, the form factor might be more like the "Huey, Dewey and Louie" robots from the 1970 era movie "Silent Running"
Sure they're cute now, but imagine if they were 20' tall and bristling with weapons
OF course even with this they will still be vulnerable to virtually everything a modern military force can bring to bear, the Mech will have to deal with everything from 500lb "Small Diameter Bombs" launched from a stealth F-35 100 km away to Infantry solders firing Javelin "Fire and Forget" ATGM's from 4750 meters. Only truly deranged or desperate people would actually approach close enough to use an RPG or Carl Gustav type anti tank weapon.
This suggests the Mech will likely have a large proportion of its carrying capacity devoted to countermeasures such as the CIWS, Trophy active defence systems and 100kW lasers, rather than massive batteries of cannons and missiles. As a mobile protective system for a land based formation, you may have found the niche for Mechs in battle.