I'll say that your accounting for minions is fair, but you aren't accounting for everything in your calculation. For things you left out of your calculation, you have 1. Potions (magic power/tipsy/archery, rage, wrath) 2. Weapon modifier 3. Weapon station buff (mainly for mages).

Here's my quick example to account for (I think) everything (basically ideal situation where you are fighting a boss with max buffs): Say you're at the start of hardmode and you have titanium armor, playing as a mage, for 23% dmg and 13% crit. We'll say you have a sorcerer emblem to add 15% dmg. We'll also assume that you are using full potions and food buffs, which means exquisitely stuffed for 10% dmg and 4% crit, rage/wrath for 10% crit & dmg, and magic power for 20% dmg. You'll also have the crystal ball for 5% dmg and 2% crit at this point. The final thing to add is having Mythical on your weapon for 15% dmg and 5% crit. I'll also add in the 7th accessory slot that you get in master mode for 28% of either crit or dmg, because if you are min-maxing this hard, you are probably playing on the hardest difficulty. So at base, we have:

armor:emblem:food:wrath/rage:mythical:magic power:base crit:crystal ball

23 + 15 + 10 + 10 + 15 + 20 + 0 + 5 = 98% dmg

13 + 0 + 4 + 10 + 5 + 0 + 4 + 2 = 38% crit

Then with 28% worth of accessories:

Menacing: 2.26 * 1.38 = 3.1188x damage

Lucky: 1.98 * 1.66 = 3.2868x damage

The difference between menacing and lucky is then a 0.168x damage multiplier, or about 17% higher damage output with lucky over menacing. To me, that seems like a very substantial difference. I will concede that, when using minions, they might compensate for that damage loss or overtake it entirely. I just wanted to show that minions aside, lucky has a substantial increase over menacing when taking all factors/buffs into consideration.

Weapon damage modifer altar base damage, which means you can't just count it as a damage bonus any damage increase you gain from a weapon modifer stacks multiplicative with damage bonuses. So this is more like

83% damage

38% crit

15% weapon modifer damage

So that's

Menacing: 2.11 * 1.38 * 1.15 = 3.35x damage

Lucky: 1.83 * 1.66 * 1.15 = 3.49x damage

So looking at the difference 3.49 - 3.35 = 0.14

So how much dps is that difference? Well lets say you use crystal storm.

Crystal strom has a use time of 7 with mythical 6 so that's 10 aps.

32 base damage * 10 aps = 320 base dps

With a mana cost of 4 and 300 mana per potion that's 7.5 seconds for every potion you drink (mana potions are easier to calculate than 'use non magic weapon while mana recharges')

mana sickness reduces your dps by an average of 8%

So 320 * 0.92 = 294.4dps

So lucky gets you an extra 294.4 * 0.14 = 41.2dps

Alright now let's look at minions.

A ruthless sanguine bat has 37 base dps, you can get 3 minions for free for 111dps.

This means that menacing gives you 31.1 extra dps from your summons

This can also be thought of as 31.1 / 294.4 = 0.106 or 10.6% of dps

So after factoring in minions lucky gets you a total of 3.4% extra damage bonus, or 10.1dps

Also keep in mind this is titanium armor specificly.

Adamatite armor has 20% damage/19% crit so its gap will be even smaller.

There's also the mixed build where you use a ada/titanium head piece + forbidden body and legs, I don't think I need to explain why this is more biased towards menacing.

Also other classes don't have magic pow potions.

Tipsy is only 10% melee damage

Archery stacks multiplicative with damage and crit so crit doesn't have any special advantage with it.

This ALSO assumes you are perfectly accurate with your crystal storm.