The bike I ride is one that has two cogs on the back hub. A static and a one-directional-coaster. cog. I use the coaster cog to commute and I do have both brakes still installed now. I did remove them once just to see if it would have any practical usage for my commute routes. I found that the static configuration was not for me. I found that the coaster configuration a lot more practical for me. I get the workout I was longing for and that on my rec-rides I will take my recumbent. 
One day I might try a few things but not for a long time.

When I rode a fixie, no coaster, I found it was hard on the knees.
I belive it’s all in the ratio you use, as not to push to hard, and
have a balance for flats and any hills. I guess I would use a flip-
flop rear wheels. But having to stop and flip the wheel, gets to
be, a pain sometimes, except on the bikeway which is usally
pretty flat. I was using a 42x 16. A fixie is the way to go, (i.e)
less maintance,less to clean after a wet or snowy ride.
As for being out of your mind, isn’t that what some people tell you
when you ride in cold or snowy weather. Lots of people think
anything out of norm, (i.e) riding a bike to work or in snow or
rain, cold is resered for carzy people.
Be safe out there on that fixie, and hope to have a good look at
it ( the fixie) sometime this summer.

This bike is at 46t chainring to a 16t freewheel. Your right about knees. I noticed that even with freewheel. Making me wonder if I made the right move. Most of of my stops have some flat areas to stop but Powhattan going south at Dorothy lane. A tad uphill take off. Other than that no knee issues.