Tonight I can write a Monte Carlo aim for this if you guys want to spell out specifics. That is, exactly what steps to follow for each turn for one fight. Then I’ll run it a million times.
Sure. I'll try to spell out a sufficiently detailed tactical plan for a computer program to execute it without the need for further input. It ends up being pretty complicated! Though if there's something I've missed, let me know.
For the record, I agree with others that this exercise doesn't really say much about the viability or lack thereof of monks in general, because every character will have good and bad match-ups. But it's kind of fun anyway.
1a. If I start my turn within 15', and have superiority dice left, I will close to melee, draw a shortsword, and make my first attack without using the -5/+10. If it hits I will use Trip Attack. Go to 2a.
1b. Else, I will make my first attack without -5/+10 with the hand crossbow. If it hits and I have superiority dice left, I will use Menacing Attack. Go to 2c.
2a. If the monk is prone, I will make my bonus action attack from 5' with -5/+10 (using hand crossbow). I will use Menacing Attack on hits unless the monk is already frightened, and precision attack on near-misses, using action surge if available to continue in this manner, dropping the shortsword for reloading purposes. Go to 4.
2b. Else, if I am within 5' and have not used action surge, I will make a bonus action attack with the shortsword without -5/+10, using Trip attack on a hit, and no maneuver on a miss. If he is prone after this, go to 2a, otherwise go to 3a.
2c. Else, I will make a bonus action attack (no -5/+10, unless he is already frightened and has used his reaction), using Menacing attack on a hit if he is not yet frightened, and no maneuver on a miss. Go to 3a.
3a. If he is frightened and (has used his reaction or it is the last attack of my turn) and isn't dodging, I use -5/+10 attacks, using precision attack on near-misses, and no maneuver on hits.
3b. Else, I use non -5/+10 attacks (with shortsword if within 5', otherwise with hand crossbow), using Menacing attack on hits, and no maneuver on misses, unless he is below about 5 x (number of remaining attacks) HP, in which case I will use precision attack on near-misses.
4. I use any remaining movement to back away, willingly provoking an opportunity if (a) he is frightened, or (b) is prone, has ki left, I am above 10 HP, and I can get more than 25' away.