TL/DR:
The preference settings that could be added to this mode sheet to hopefully clean this up are:
joystick_dead_zone_shape and joystick_deflection_minimum. Set the shape to 0 for square, and the minimum deflection to something like 10.
There are several different things going on:
Two active inputs are conflicting over control for the same output:

If the up arrow is activated by the up joystick, then it cannot also repeatedly turn off and on. If it is in the middle of a repeat cycle, then the "normal" up row triggers, that will cancel any repeat timer. Two different output functions cannot simultaneously control the same output and have predictable results. Normally this is not a problem with two different sip/puff inputs because only one sip/puff can be active at a time. The joystick or lip input can be active at the same time as a sip/puff and cause a conflict.
Arrow keys are also paired with their opposite for some functions. Up and down are a pair, and left and right are a pair. Simultaneously activating up and down at the same time, which could happen with this setup, could produce undefined results.
If you are not using a square dead-zone with the joystick, it will be nearly impossible to only active one arrow key. You will always get two keys. It the joystick is moved to the left or right, an up or down arrow key will also be pressed. The joystick might be 50% to the left or right, but it will also be 0.001% up or down and anything greater than 0 is the same as fully on 100%.
Circular dead-zone works fine for a mouse pointer, but not when driving discrete on/off keys or buttons.
The quadstick reports up to six regular keys being pressed at the same time, plus up to eight modifier keys, like control, shift, alt, widows, ect. It only sends a report when something changes. The operating system converts those reports into key-down events and key-up events. Then the emulator will listen for those events and convert them into something the game can work with. There are layers after layers of code that are interacting to produce the final result for a game program written when memory was purchased in kilobits and is far from its native environment. Who knows how it will react.