If I make the string longer, should the body be proportionately longer also?
Yes. 1200 mm for a full size bass versus 1100 for a 3/4
If the string is longer (42-43ish), should the fingerboard be wider to keep the strings from hitting each other? Or will the increased tension on a slightly longer string (of the same gauge and material and tuned frequency) adequately diminish the lateral vibration?
Yes make the spacing wider, string 1-4 spacing at nut should be 33mm and at bridge 92 versus 30/84 for 3/4. I don't know about a five stringer. Ask Paul what his measures.
I have observed significant variability of width of the lower bout and less variability in the upper one. Is there a formula for these proportions, some mathematical model to follow? I see significant variability in the arch height too. For instance proportionally, a 1.25" arch and a 1.75" arch are really different, but I've seen both.
No formula, you will just want to be able to reach around the thing. A proper amount of air volume will help low end support. To get the ideal support from the air (helmholtz) mode on a DB it would need to be huge, so it is a compromise. The ratio of upper bout width to lower is not important really, just the overal internal volume. Make it a big sucker if you can handle it. See Arnald Schnitzer's ergonomic bass for for more hidden info.
If I change the angle of finger board to top, this seems to have more radical implications because it will alter the ratio of the component force vectors produced by string tension. As the angle over the bridge becomes more acute the component squeezing the top between the saddle and the neck end block becomes less and the opposing component (approx 90 degrees apart) vector that puts downward pressure on the bridge and top becomes greater. Is there an optimal equilibrium angle across the bridge? Does it depend on the stiffness of the top, etc.? How do we determine, other than a tried and true plan what that angle should be? Most importantly, Is it different for 5 strings than 4? Or since the component vectors essentially oppose each other, one squeezing the top and tending to swell it at the bridge and the other pushing it down, does the tension of the additional string cancel out and just affect the rigidity of the ribs, back, and neck? Does making the bridge taller give the strings more leverage on the top?
Start with what's important i.e. the bridge height. (fb height extended to bridge is 169mm for a full sizer). That is going to effect tone, playability and volume, the three musketeers of good bass design. You can alter the string angle a little then by changing the saddle height. Sounds like you really do understand this concept from you questions.
Yes. 1200 mm for a full size bass versus 1100 for a 3/4
If the string is longer (42-43ish), should the fingerboard be wider to keep the strings from hitting each other? Or will the increased tension on a slightly longer string (of the same gauge and material and tuned frequency) adequately diminish the lateral vibration?
Yes make the spacing wider, string 1-4 spacing at nut should be 33mm and at bridge 92 versus 30/84 for 3/4. I don't know about a five stringer. Ask Paul what his measures.
I have observed significant variability of width of the lower bout and less variability in the upper one. Is there a formula for these proportions, some mathematical model to follow? I see significant variability in the arch height too. For instance proportionally, a 1.25" arch and a 1.75" arch are really different, but I've seen both.
No formula, you will just want to be able to reach around the thing. A proper amount of air volume will help low end support. To get the ideal support from the air (helmholtz) mode on a DB it would need to be huge, so it is a compromise. The ratio of upper bout width to lower is not important really, just the overal internal volume. Make it a big sucker if you can handle it. See Arnald Schnitzer's ergonomic bass for for more hidden info.
If I change the angle of finger board to top, this seems to have more radical implications because it will alter the ratio of the component force vectors produced by string tension. As the angle over the bridge becomes more acute the component squeezing the top between the saddle and the neck end block becomes less and the opposing component (approx 90 degrees apart) vector that puts downward pressure on the bridge and top becomes greater. Is there an optimal equilibrium angle across the bridge? Does it depend on the stiffness of the top, etc.? How do we determine, other than a tried and true plan what that angle should be? Most importantly, Is it different for 5 strings than 4? Or since the component vectors essentially oppose each other, one squeezing the top and tending to swell it at the bridge and the other pushing it down, does the tension of the additional string cancel out and just affect the rigidity of the ribs, back, and neck? Does making the bridge taller give the strings more leverage on the top?
Start with what's important i.e. the bridge height. (fb height extended to bridge is 169mm for a full sizer). That is going to effect tone, playability and volume, the three musketeers of good bass design. You can alter the string angle a little then by changing the saddle height. Sounds like you really do understand this concept from you questions.

We're losing the wrong Georges!!!!