High on grid // "allweaponsdod6damage but..."

 I'm running a game for friends who want to play D&D because they saw it on Stranger Things. They are in for the minis and they want to play with them because they use them on the show, no negociations. At first I tried to tell them that miniatures are optional, that I never used them. But they passed it on me in the end: I thought "what the fuck why not" and now I'm searching for cheap second hand warhammer Rohan warriors. 

Though I started playing rpgs with grids by drawing little combats in a squared notebook, I've trained myself to use abstract combat afterwards. But now that I'm bound to use it, I'm trying to devise ways in which to use it to its greater potential. I don't want to change things that are not broken (not re-defining combat or anything). But there are nebulous things that could be improved.

As in Basic D&D all weapons do d6 damage, the distinction between weapons could be how do they behave on a grid (ranged weapons already work that way with the "short-medium-long" ranges)

Spears, for example, could use their long shaft to strike in all directions, including diagonals (red and yellow arrows) while shortswords can only strike in the cardinal directions (yellow arrows). This makes swords and spears equally functional on 1 square wide corridors (which makes a lot of sense). You can make spears so they can also attack things 1 square away in the cardinal directions. Maybe is too unrealistic but if it follows game logic its OK for me.

Two handed swords and greataxes can affect all guys on an L shaped area around the wielder (because an L looks to me shaped like a slash), like in this picture, highlighted in green. This can work with systems with variable weapon damage by having the sword doing d8 damage to one target OR d6 to all in that area. Or maybe straight d8 in area.

Certain magic swords can also strike on cone or square area (a sword capable of summoning whirlwinds or sending flame waves, maybe) and certain magic items could improve your movement rate by some squares per turn (all the humanoid monsters/pcs have similar movement rates: 2 or 4 feet in combat, though I abstract it in 2 or 4 squares because I'm european and I dont want to learn what a feet or a yard are). Having a +1 square per turn is the edge to outrun that monster that moves just at your same rate.

Every other problem that arises with the game, I'll try to solve it or balance it by making up shit with the grid. Let's see what happens.