I did exactly what you said - but it will not connect (Connection Refused). I did some more digging and it looks like the Android Box's core OS has to have SSH enabled, but when you're doing this "boot method", you don't have access to it. Sounds like side loading / adb might be the only way to load everything.
As noted above, one of the key concerns I have is knowing if LibreElec is a ROM that will overwrite the stock ROM so it boots into Kodi by default. If I need to do the toothpick trick every time and reset everything, that is not a solution.
The LibreELEC image is not a ROM, it is just an operating system image that contains the kernel, root filesystem and dtb. If you run it from external media, it will not overwrite anything. The toothpick method only loads the autoscript on the card, which allows the bootloader to boot the OS from USB and SD card instead of eMMC, if it is connected, otherwise it will still boot from eMMC.
The toothpick method only needs to be done once, after that it will always be able to boot from external media, unless Android receives a master reset command, because that can overwrite the boot script changes. Also, if I may suggest, try using an SD card instead of a USB flash drive, because the USB is much more problematic.
The basic problem with your description is that it is not clear whether LibreELEC is running at all when you try SSH, whether you are trying with the IP address of the box, whether the network is working on the box at all, and whether SSH is definitely enabled or not. Instead, you mention things like adb and sideload, which are absolutely not needed for LibreELEC.