Soldier uniforms need to be functional, and while some of the uniforms used historically don't
seem functional, they were.
One of the first questions that need to be asked is 'are they using sulfur+saltpeter+charcoal gunpowder or a more technologically complicated lower smoke output powder.' Or even guncotton, if that can be sourced. This matters a
lot, because 19th century uniforms and earlier were very colourful because the thick smoke of sulfur holding gunpowder made identifying
anything from a distance nearly impossible, so having a blob of colour that stands out is useful.
Another early question you need to ask is 'what's the local fashion like?' It may sound silly, but you want to design a uniform that mostly fits with the local clothing traditions. It means you don't have to teach tailors and weavers how to make those uniforms and can instead send in soldiers immediately.
3rd. It's entirely alright
not to make a complicated uniform adjustment. First think of what a soldier will
need, and a soldier in Greyfalls will have a very different battlefield to face than soldiers using such weapons did in the mid 19th century. He'll be facing armies used to, expecting to face and using swords, spears, axes, bows and shields. He'll need armour because
armour is useful against weapons like that while against breech loading guns most armour the enemy will be using will be useful only at a distance. It might actually be easiest to take the armour of a Greyfalls' bowman, which is likely some form of mail or scale armour, and exchange his bow and quill for a gun and ammo pouch. Put a colourful tabard like garment on top for identification purposes in dense smoke and it's done.
JSDF will be pushing for guns and basing their training on what they know. There are a few historians in the group and at least one military historian, so there will be some influence there as well. General tactics will probably mirror those of the mid 19th century, mainly due to limits imposed by equipment, materials and the foes they expect to face.
Something that should not be neglected in that case: Armies Greyfalls is likely to face are armies that are
expecting to engage in melee. Greyfalls should consider bayonet drill a critical component of their soldiers' training regimen.
Also important: Warfare in the mid 19th century is a
very different beast from early 21st century warfare. Communication is slow, getting a good view of the battle is nearly impossible, your fastest troops are horse cavalry, your cannons are short range howitzers and your indirect fire capability is a bunch of short range mortars.
There are no cars, nor trains, nor aircraft that can move troops or information faster than a horse can gallop. And your logistics train is
slow as molasses, compared to 21st century combat.
