How to Make a Bow-Kata Monk/Fighter?

[SociopathFriend]

However, the point wasn't to dispute your logic. It was to further support the feat as a very solid option for your build regardless of its name, 'Crossbow' Expert.

As for the whole concept, I'd say you have it about right: Kensei/Battle Master would be quite handy combination for what you're trying to accomplish, especially if you want to avoid using magic.

I admittedly had messed up what the Crossbow Expert feat does. It isn't 100% based on shooting someone within 5 feet with the bow- it's based on being able to shoot anyone anywhere with a bow while you're in melee (typically 5 feet).
I don't think my DM has ever brought that up in all honesty which is probably why I never thought of it correctly. Disadvantage with ranged attacks on someone within 5 feet yes but I dunno if he's ever imposed it for shooting someone elsewhere when in melee.

I most certainly would consider that an important feat in these newfound circumstances- depending on whether my DM is doing that deliberately or not. It's something of a coin-flip.

Since you can't always count on getting your hands on a magic longbow, I'd say you should aim for at least 6 levels in Kensei. Since your weapon of choice is the Longbow (d8) it doesn't really matter if your Martial Arts die doesn't get any higher from there, since you can always make the choice yourself: whether to use the weapon's die or the Martial Arts die. After 6th level, you could take 3 or 4 levels in Battle Master. Maybe more if you don't mind getting one slightly redundant level (fighter 5th) due to multiple Extra Attack features not stacking. 6 ki points/sr is quite alright when you also have 4 superiority dice/sr.

I definitely wanted at least 1 level of Fighter so as to get the Archery Fighting Style and the bonus to-hit but it does seem like diving fully into the bow-wielding Monk offers a good bit too.