1) how do you prevent the loose tether ends from flying around when not in use (as you're only on 1 at a time, or 2 while in transition)?
I clip the tether to a fitting on the mast or at the cockpit.
2) Is your cabin top padeye centered, or do you have one on either side of the cabin top that you'll choose based on tack?
I have mine on the cabin top near the companion way. I do not have a dodger on my boat. With a dodger you would need to locate the padeye to one side. I always go forward on my Starboard side due to furling line running up the Port side. It is my preference. With a dodger you would need locate the padeye ahead of the dodger and to the side so you can wrap the tether around the side of the dodger and reach it form the cockpit.
3) Do you have a single line from bow to mast to cabin top, or is this two lines (each starting from the mast)?
Yes a single line. It was longer than the boat length so easily makes the trip 2/3rds of the boat from bow to cockpit. John Harries includes some ideas on make it your self jacklines. Provides a resource to the webbing material. I do not have it available at the moment. I'll look in my data. You can make your own jacklines or buy them pre-made. I bought Lewmar jacklines.
4) Where (exactly) is your cockpit padeye? I'm wondering how you navigate the cockpit during tacks, around the pedestal, etc.?
I put the padeye in front of the binnacle on my boat. The tether is long enough for me to move about the boat cockpit. Solo sailing, I have to step in front of my binnacle to tack the boat. It is a bit of a dance. You learn what works and adapt your choreography to fit your needs. Again, I generally move around the binnacle on the starboard side. So the tether follows behind me.