This again? Eh, OK.
Being slow and having no range attacks is a problem. But rather than rewrite the rules to favor slow and melee only, I would suggest maybe fixing it by either:
a) stop being slow.
or
B) get a decent ranged attack.
I play a 14th level hill dwarf who wears full plate and wields a greatsword. He kicks ass and not many things can keep away from him. Why? Because I made sure he could get to his enemies.
His classes: Fighter (Eldritch Knight) 8/Warlock(Fiend/Chain) 6. He can Misty Step or Fly as needed, he can cast Haste off of a scroll, and in another level he'll be able to Dimension Door himself and one other person. Once he gets in your face he has the Sentinal feat to make it hard to run away.
There's been more than one fight where he's used Misty Step to jump behind the front line and start tearing up the enemy casters. He'd use a greataxe, but he found a Legendary Greatsword, so he uses that instead.
He also has Counterspell and Dispel Magic ready to go. Basically his magic is meant to get him past any obstacles and within sword reach of his foe.
Plus, if I don't want to spend the spells, he can Eldritch Blast (his Charisma isn't that great, but it's still 3 ranged attacks.)
And if you don't build your axe dwarf to be a spellcaster...well, this is a team game. It's not only melee and ranged characters.
Hopefully you aren't by yourself and actually have a wizard or sorcerer willing to either lay down Fog Cloud (so you can use it as cover while you close) or cast a crowd control spell on the ranged opponents to give you time to close...or cast Fly or Haste on your, or Dimension Door you up to them.
I've played casters, and sometimes the best use of your magic is getting your melee monster into range. (One time in 3rd edition I cast Dimension Door and moved the three melee fighters within 5' of the big monster on on the first round of combat - so they could all full attack instead of moving and getting a single attack. The poor thing never even got a chance to attack. )
Being slow and having no range attacks is a problem. But rather than rewrite the rules to favor slow and melee only, I would suggest maybe fixing it by either:
a) stop being slow.
or
B) get a decent ranged attack.
I play a 14th level hill dwarf who wears full plate and wields a greatsword. He kicks ass and not many things can keep away from him. Why? Because I made sure he could get to his enemies.
His classes: Fighter (Eldritch Knight) 8/Warlock(Fiend/Chain) 6. He can Misty Step or Fly as needed, he can cast Haste off of a scroll, and in another level he'll be able to Dimension Door himself and one other person. Once he gets in your face he has the Sentinal feat to make it hard to run away.
There's been more than one fight where he's used Misty Step to jump behind the front line and start tearing up the enemy casters. He'd use a greataxe, but he found a Legendary Greatsword, so he uses that instead.

He also has Counterspell and Dispel Magic ready to go. Basically his magic is meant to get him past any obstacles and within sword reach of his foe.
Plus, if I don't want to spend the spells, he can Eldritch Blast (his Charisma isn't that great, but it's still 3 ranged attacks.)
And if you don't build your axe dwarf to be a spellcaster...well, this is a team game. It's not only melee and ranged characters.
Hopefully you aren't by yourself and actually have a wizard or sorcerer willing to either lay down Fog Cloud (so you can use it as cover while you close) or cast a crowd control spell on the ranged opponents to give you time to close...or cast Fly or Haste on your, or Dimension Door you up to them.
I've played casters, and sometimes the best use of your magic is getting your melee monster into range. (One time in 3rd edition I cast Dimension Door and moved the three melee fighters within 5' of the big monster on on the first round of combat - so they could all full attack instead of moving and getting a single attack. The poor thing never even got a chance to attack. )