I like that a lot.
Paladin Divine Smite + their additional spell slots works better than the Elidritch Smite invocation which only allows warlock slots to power it. But with curse only working on one foe per short rest, I wonder if Champion 3 for all crits on 19-20 isn't a better way to go first, and then swing back to paladin.
Note that if you also pick up Blade Pact you can extend two handed weapons for a larger crit die. And then GWM can give you a bonus action attack with it on crit for extra fun.
I've tried going a DEX paladin route, with Oath of Vengeance plus eventually the Mounted Combat feat for regular advantage. Divine Smite on crits is the biggest reliable non-weapon dice I can find to add. (Rogue SA you have the question if you hit but not crit, if you want to apply SA to deliver it, or roll again and hope you don't miss.) But finesse limits my weapon damage die to max d8.
I think your Hexblade version works better.
If you crit building see if you can get a party mate to cast Shadow Blade for you. Finesse weapon with 2d8 dmg die and expanded crit range in dim light can't be passed up.
Shadow Blade only has a range of Self. Plus, we're really only looking for things you can do by yourself.
But I have a really good idea.
Go Rogue 3, Arcane Trickster. Pick the Find Familiar spell. Your familiar can use the Help action every turn to give you advantage on one attack.
At Rogue 4, pick up Elven Accuracy feat, and voila! You're crit-fishing at level 4, with Sneak Attack no less! And just keep building on it.
Then go Rogue 4/Fighter Champion 3 or 5. If you only go 3 you get: a fighting style, action surge, and a 19-20 crit range. If you go 5 you also get: an ASI( I suggest Defensive Duelest for survivability, or Lucky to make SURE your attacks hit ), and an extra attack.
At Rogue 7/Fighter3-5 get Shadow Blade. Or you can choose to Fighter 15 for crit 18-20 and Extra Attack(2).
If you go Rogue 13/Fighter 3-5, you can use Mage Hand with a bonus action to give yourself advantage on all attacks against a single opponent for a turn. Alternatively, go to Fighter 11 and get Extra Attack(2). But I think it's better to go Rogue most of the way for Sneak Attack.
Most familiars have 10 AC and 1 HP, usually if a DM notices you're using the familiar in combat for the help action (which is melee ranged) they'll flatten your familiar in one swing from a monster.
The biggest draw is that Bards are the only full caster class that can get both Elemental Weapon and Extra Attack. Elemental weapon cast from a level 7 spell slot adds 3d4 damage to each hit (average 15, or 30 on a crit)
I like the new 5th level Holy Weapon for 2d8 per attack myself, with one casting lasting up to an hour. But you can either have full attack (paladin, so level 17) or full caster (cleric or divine soul sorcerer at level 9). Or the same trick, of using bard's magical secrets to pick it up.
Can anyone do a mathematical breakdown of the different builds for damage outputs?
I could but I would need a target AC. I don't have the DMG so I don't know what the average AC of a monster is at a certain level.