I think the most difficult criterion here is the weight limit, and the set idea that it has to be a flatbed. Rear focusing could be an issue as well. Is that a weight limit imposed by some rule, or just something you are personally aiming for? If not for that, I would just suggest that you backback with a lower-end monorail, since there are so many specific requirements for movements and extension that you list. There are many that fit the bill, and they are cheap compared to what you are talking about. I used to backpack a GVII a lot, and it was very convenient (and light, not to mention that a tripod head was not necessary with this camera, as it has its own dedicated - and very light - head). A cheap modern Cambo, Toyo, Omega, etc. will work as well. I have backpacked with a borrowed modern-style Cambo as well, and it worked out OK. I backpack my Sinar F-1 now, and it is plenty doable, and even more compact than the GV or that Cambo I tried out. It also does not weigh that much. There are adapters to Linhof boards. There is no screwing around this way worrying about what features and specs the camera has, because it has them all.
As for weight, I would think about lenses, film, tripod, and head more than the camera itself. You can put a multipurpose standard on the front to reduce weight (making it an F-1 instead of an F-2), instead of a focusing standard. Slower versions of lenses are the way to go in the field, IMO. I wish I had more of them myself, as the only drag about backpacking the F-1 is the big, heavy glass that I have for it. If you are talking about spending custom Ebony bucks, I think you would be better off using that money for a slew of lightweight glass for the field. As for film, I feel the same way: If you can afford custom Ebony bucks, go for Quickloads. Same with tripods.
I assumed this was for backpacking, but it was not stated by you that I read. What are you going to use this for?
Another thing: What do you mean by "axial and base tilts"? I thought it was one or the other, unless you have something like a Sinar P, which does both (coarse base tilt and fine axial tilt). Must be a feature of some wooden cameras, which I do not know all that well.
I just weighed my F-1. It is just under 6 lb. with a 12 inch rail and no lensboard. There is a Sinar low profile rail clamp that might reduce the weight even more. An extension rail would add some weight as well, as would a Linhof adapter. Let's just say 7 lb. to be conservative. A seven pound camera is heavy, but not the most horrendous price to pay to not have to worry about what features it does or does not have. It has as much extension as you want, as much movement as you want, whatever bellows you want, the movements that you don't need will not make the camera more rickety, and it has rear focusing. It will also let you use barrel lenses in the field, if you get one of the various behind-the-lens leaf shutters. This also gives you total shutter consistency lens to lens. Additionally, you can't forget to cock the shutter. If you use both cables (which I personally never do, as it is too much of a tangle), you don't even have to remember to close the shutter before pulling your dark slide. I am basically trying to say that the camera is very quick, convenient, and nearly fool proof; great attributes when racing against changing light out in nature.
One thing it does not have is axial tilts. This does not bother me, since the camera has both coarse and fine focusing that are very quick to operate from behind the camera. It is very quick to push the rear standard in to make up for the defocusing caused by tilting the front standard.
KEH has a BGN condition Sinar F for $245 right now.