Having built two full size Gribeauval carriages, the splayed carriage is fairly easy to construct. All the mortices on the cheeks them selves are the same depth and standard to cut. The tennons or the bolsters between the cheeks, have the ends cut at an angle. Not really hard joinery. If the workshop is set up to make the carriages, then KISS would apply here.

The awkward bit is not the timber work. Its drilling the holes through the carriage and bolsters for the iron or bronze bolts. To get the angles correct takes some judicious packing of the carriage on a surface. With a parallel carriage, the drilling is simplicity its self. However this does not seem to have been a major issue as the French produced thousands of carriages to this design. As did most nations in Europe prior to 1810/1811. So construction issues do not seem to have been a problem.

There are a number of issues however, that have not yet been mentioned in this discussion:

1) With a parallel carriage, the gun tube needed rimbases to keep it square on the carriage, On a splayed carriage, the shape of the carriage would keep the gun tube in place and rimbases were perhaps not as essential. With a parallel carriage the rim bases can be at right angles to the tube and not tapered. Perhaps making the tube easier to cast.
2) Also with a parallel carriage, one can use the side of the gun tube for a quarter site, which you can not do with a splayed carriage, as the front of the carriage blocks the view of the muzzle end.
3) With a parallel carriage, a larger calibre of howitzer tube can be carried as the carriage has more space for the gun tube.
4) the cap squares and other iron work can be wrought easier at right angles than at an angle.

So in my mind, there are a number of different factors that influenced the change from splayed to parallel and not just the need to carry an ammunition box on the carriage, which yes is a reason but one Gribeauval over came by having a recess in each cheek to take the box.

Argubly therefore, this need to have a parallel carriage to mount an ammunition box cannot soley have been the reason for the adoption of the parallel carriage.