Sure, longer pins do exist:
An alternative is to have male pins on one side and female pins on the other:
Searching for "GPIO 2x20" in your favorite shopping site should give you similar results.
In both cases, you may need an iron which is thin enough to go between the pins to make sure the solder flows evenly around each pin.
You might be interested in Stacking headers (eg: https://www.adafruit.com/product/85)
Several boards all with stacking headers can be connected on top of each other, including to a breadboard at the bottom of the stack too.
Photo example to illustrate, just an arbitrary google images result:
There are really two parts to this question. Can you boot from floppy, and can you put an OS on a floppy.
As to whether you can put an OS on a floppy, yes of course you can. Quite apart from the good old days of MS-DOS 3.1, CP/M, et al, I have written small OS that will run from a floppy, it isn't difficult.
As an intellectual exercise or learning process, ...
It is unclear exactly what you have done (list full code & connections).
What is R_US
The fundamental problem is your circuit.
Using an emitter follower is POOR practice; it will attempt to put 2.7V across the LED when ON, overloading the GPIO with unpredictable results. You have shown the LED connected in reverse.
Try a more conventional circuit; the ...
You can get extended headers - I use these on my Pico so it plugs into a breadboard but still has accessible pins.
NOTE this will not let you use 2 HATs (as the pins would be inverted).
The normal solution is to use extended headers on the HAT.
You can only control two servos independently with the Pi's hardware PWM.
GPIO 12/18 share a channel.
GPIO 13/19 share a channel.
The same settings apply to GPIO which share a channel.
E.g. If servo1 is on GPIO12 and servo2 on GPIO18 they will get the same signal (same frequency, same pulsewidth).
pigpio supports the hardware PWM features of the Pi. So you ...