Yes! Most likely insane-Welcome to the club!

I have been contemplating doing much the same thing as you. Currently the debate is between double fixed or the Rohloff 14 speed hub for a geared alternative to full-load touring. Both would offer relief from the obsolete rear derailleur, and give the benefit of a symmetrically tensioned rear wheel, true chainline all the time, and the possibility of a chain case to compelete the drive chain protection.

What makes me think that the fixed option has a rational aspect to it is:

1-Better against wind. Yesteday, I rode against a hard headwind, in the rain,-70" gear, about 55 k. I was attemting to get to the base of a hill that on a geared bike (59" low gear) would normally take 20-30 minutes to ascend. I had to abort the attempt since I had a scheduled pick-up arranged, and a rear-wheel flat had necessitated a course adjustment. But the thing that stood out was that the wind was not nearly as defeating as I remember it on my geared bikes in the past. I always regarded wind as way worse than hills anyway, yet I can honestly say that by pedaling through it on a fixed made the experience if not enjoyable, at least tolerable.

2-Coasting does not equate to "resting" in the restorative sense.

I had the idea that over the same distance, that riding fixed would be more taxing than geared riding, since you would not have the benefit of those mini-breaks while coasting. I had heard comments along the lines of " your legs will feel like spaghetti after one hour or so." The remarkable thing is that my legs felt fresher on the fixed after the same distance, than they did on the geared bike the day before. I concluded that the effort to bring the legs back up to speed after coasting may have been more costly energy-wise than pedaling full time.

The Fixer on a recent thread posted the link to a German cyclist who navigated the U.S. on a double-fixed with 44-17 (69") and 44-18 (65") on a Goldtec rear hub while pulling a German Yak-type trailer with a Schmidt dynohub.

So, what you are considering is certainly doable. I guess whether it is preferrable is the question.