Giving advantage when two characters are within melee distance of the same enemy and to ranged attacks against enemies already engaged in melee would be a nice replacement I think
These would give way too much advantage to enemies since there is usually more of them than our party of 4. I agree with others that you should get advantage for flanking when you have party members on opposite sides of the enemy. Or maybe even only a +2 to hit. Since this is a video game, the computer can easily do all those small calculations that 5e tried to let players not worry about.
Your point about ranged attacks is interesting. Most systems, including past d&d versions, actually give a penalty for shooting into melee combat. True, 5e did away with this, but saying that these attacks should actually get a bonus is too much imo. Maybe it'd be fine if you only got advantage for shooting the back of an enemy while they are also facing a melee threat on their front. That could encourage some interesting positioning of your tank: sending your tank deep into enemy lines so that enemies turn around to face him, exposing their backs to your archers. You'd be allowing your tank to be more easily flanked and ganged up on in exchange for advantage on ranged attacks, which is a nicely tactical decision.
