I will be changing the fork from 55mm rake to 44mm rake (for other reasons). Will this help significantly?
If you're trying to improve straight line stability in crosswinds the shorter rake fork will increase, not reduce, the amount of steering input needed to keep your tandem tracking in a straight line.
Remember, on a tandem, shorter rake makes the tandem more responsive to lean angle and countersteering inputs. Santana, Trek and others use 55mm of rake to reduce the captain's task load with respect to things like stoker movements and minor changes in lean angle whereas Co-Motion, for example, has always used 50mm of rake on it's steel forks for what has been characterized as more sport / race-oriented handling and responsiveness to leaning inputs... making their tandems "feel" more lively and reminiscent of a single road bike. Co-Motion and others have taken this a few steps further on their racing tandems by spec'ing forks with 45mm or 44mm of rake.
Would a theoretical fork with NO rake handle completely neutral?
55mm rake w/73* head tube = 4.9 cm of trail (Santana / Trek w/OEM steel fork)
53mm rake w/73* head tube = 5.1 cm of trail (Cannondale)
50mm rake w/73* head tube = 5.4 cm of trail (Co-Motion w/OEM steel fork or Trek w/OEM carbon fork)
44mm rake w/73* head tube = 6.0 cm of trail (Calfee or Co-Motion w/Alpha Q fork)
0mm rake w/73* head tube = 10.6 cm of trail
Zero rake would obviously present a wheel/frame/toe clearance issue on any bike not specifically built for it and would be of no practical use on a road tandem. So, assuming a 73* head tube angle, it's probably a moot point. If, however, someone was so inclined to design a frame around a zero rake fork they could probably find a head angle that would create the necessary amount of steering trail to make the tandem handle to suit the team's needs.
Our rims are about 31mm deep with 24 fat bladed spokes. How would it compare to a 21mm Aerospoke with 32 round spokes - like Zonatandem's front wheel.
As mentioned in the other thread about wheels, this may be getting to the crux of your issue if what you're trying to address is how the lower number of paired, flat-bladed spokes react to crosswinds vs. a more conventional higher-count round spoke network. Again, from the other post I offered this in response to your follow-up question which introduced "easier to handle" as a criteria as well as your point of reference, a set of paired spoke wheels:
If you remove the flat bladed spokes from the equation and are only comparing a set of wheels with 36 spokes that has a 30mm deep rim vs a 22mm deep rim then there will be a difference in wind side loading. However, the degree to which the additional side loading would be detremental to handling would seem to be pretty subjective based on rider sensitivity, i.e., some riders will know if their tires are 5lbs low on air, whereas others might not know they are 20 lbs off. The best way to find out would be to simply borrow a conventional front wheel and use it on your tandem. There's nothing "tandem specific" about a front wheel unless a team's weight demands something greater than 32 or 36 spokes, e.g., 350 - 450 lbs, respectively for non-technical terrain.
That depends on your definition of "easier". That notional 48 spoke wheel might have a higher side loading and be experiencing more of a push effect from a crosswind; however, it probably exhibits less buffeting or "pulsing" than a Shimano Santana Sweet 16 or Rolf Prima Vigor (and perhaps your Bontragers?) since the loading is distributed on 48 small and round spokes vs. 16, 20 or 24 flat bladed spokes that are paired together in 8, 10 or 12 places around the rim.
The latter may be the real issue you're trying to address -- the effect of crosswinds on bladed and/or paired low-spoke count wheels -- not simply the differences between a semi-box section 22mm deep rim and a 30mm deep rim with conventional and round spokes. In that vane, then yes... I have found the Rolf's to be 'twitchier' in a crosswind than our other 30mm deep wheels with more conventional, non-paired and higher count spoke networks, e.g., 36h Deep-Vs, 36h Fusion and our 24h Topolino AX3.0-Ts (which probably have as much spoke surface area with respect to crosswind loading as a pair of 40h wheels).
However, bear in mind, from a performance standpoint having a low-side load doesn't necessarily equate to lower overall drag. The trick is balancing an acceptable level of low drag against any negative characteristics of the side loading, e.g., a tri-spoke or very deep aero wheel is still faster in a crosswind vs. a conventional or semi-aero wheel but can become too difficult to handle. It's all about trade offs.
Therefore, if you really aren't interested in the very slight aerodynamic advantage your current semi-aero wheels afford to you there are a lot of really good reasons to set them aside for a conventional set of wheels. Getting rid of that slight twitchiness that you seem to be experiencing in crosswinds might just be one of those benefits. Others include lower overall ownership costs, ease of repair, replaceability of parts, no obsolescence issues, etc..
Would the side profile difference be of any significance.
It is, but as noted there's more to consider than just the rim's depth.
You can find data on side force and drag coefficients that compare conventionally spoked wheels to the more aerodynamic wheels at these links.
John Cobb's aero data:
The side force data is near the bottom and a GL330 is a box rim.
Rolf's wind tunnel data:
Are there other mechanical factors?
Just remember, when you're trying to address crosswinds on a moving bicycle you need to look at the wheel from the perspective of how it is influenced by the apparent wind, not the true wind. For the folks who have learned to master sailboats or who fly aircraft, it's a pretty straight forward thing. However, for anyone who hasn't thought about how the difference HED cycling as an excellent article and a web-based tool that lets you experiment with different riding scenarios to see how wind velocity and direction are altered by the movement of the bike: http://www.hedcycling.com/technical/yaw-calculator.php