So... my intended vote and why.
[ ] Federal Alchemic
[ ] Reject [Shipyard]
[ ] Reject [Cold Springs]
[ ] Walt-Hewlett
[ ] Valois Model 1897 76mm
[ ] Walt - Bolt action, five round integral magazine, generally competently made short rifle.
The reason for Federal Alchemic instead of Watt and Henderson is that, on average, it's six 50 sided dice to complete. With Federal Alchemic, that's 40 Resources over 2 turns, with Watt and Henderson it's 45 resources over 3 turns. If the rolls are low and another roll has to be made, it's 60 resources over 3 turns, or 60 resources over 4 turns, in which case, while cost is the same, it's still completed a turn earlier.
Rejecting both the contracts for the shipyard and the armoury because they are just terrible contracts.
For the machine gun, going for Walt-Hewlett as we are looking for something mobile while their performance is otherwise not that different AFAICT. If we were looking for a fortress machine gun I would be more interested in the Hochmann or telling the army to buy some navy machine guns.
For the artillery we're going with the Valois 76mm, the army wants something to do field gun things with, moving around the battlefield at speed and cutting down troops in the open. This fulfills that requirement quite well. I would've preferred a Vinlandic design, but apparently our artillery designers are being a bunch of muppets.
For the carbine I'm going for the Walt. While I would've preferred the Chatam, the carbine is intended to be rolled out more widely than just the cavalry, and instead be provided to support troops in general as well. Such a wide roll out would make the Chatam a little too expensive, while the Walt is also noted as being suited to upgrading to a higher velocity round, which will be useful in the future.