Ha, this one was just to test, but it can get pretty fun with Eldritch Knight 7/Wizard 4. You still get 3 feats and you count as a 6th-level spellcaster, letting you scribe 3rd level wizard spells. You can take Dueling fighting style and go torch/shield with Shillelagh super-charging your torch - with 20 INT, it's dealing 1d8+7 bludgeoning + 1d4 fire. You might consider dual wielding, but Shillelagh only works on your main hand weapon unfortunately. You can cast a cantrip and still attack with your bonus action, so in tough fights you might consider True Strike or Blade Ward, depending on if you need to hit or take less damage. You have extra attack, so you can swing twice if you'd rather.
If you take your last level in Eldritch Knight, you get one more feat - I like War Caster since you'll be able to get use from both the concentration advantage and Shocking Grasp OA. If you take your last level in Wizard, you count as a 7th-level spellcaster and can scribe 4th level wizard spells. Either way, it's a pretty decent gish build with a lot of flexibility.
Pretty sure it's just "whatever is highest" for Shillelagh between Int, Cha and Wis. Got any screenshots from your testing where as an example a Rogue has Int being used despite having a higher Cha? Your Tav for example has a 20 Int, so Int is highest.
Edit: Also FWIW any class can snag Magic Initiate: Druid and grab the Cantrip if they don't want to dip into Druid or Nature Cleric to snag it, not that it's typically the optimal feat choice but it's certainly an option.
Sure, I tested that real quick. Here's a 4th level fighter with higher CHA and WIS than INT, but Shillelagh still uses INT.
![[Linked Image from i.imgur.com]](https://i.imgur.com/HuKmWmC.png)
If you multiclass, then it will use the highest spellcasting ability from your multiclass. For example, I added one level of barbarian (which has CHA spellcasting ability) to this, and Shillelagh then used CHA as the modifier.
I think Magic Initiate: Druid is the one of the best feats you can grab for building a gish. You can grab both Shillelagh and Guidance or Resistance as useful cantrips, and for your once-per-long-rest spell, you can take Longstrider or Speak with Animals, both of which only need to be cast once per long rest anyway. If you're multiclassing just for a dip, it's usually a choice between the dip and a feat anyway. I generally prefer taking the feat so that abilities that scale off of class level can continue to gain benefit.