Nitori as commander of artillery, just to be cautious do not let her get too much exited...
patchouli definitely gotta be there as a master mind she can definitely proves herself to be worthy in the long terms,
now a bunch of cirnos can be useful, they are cheap and since its an ice fairy and we know napolionic armies do not pair well with cold people lol can be use somehow
another bunch of sakuyas absolutely in, lethal for special missions
aya is reckless, with her background as journalist she knows pretty well the topography of gensokyo, she is worthy
marisa is also reckless and very outgoing life style, beside in the games she always get the traits of faster and best firepower, if the group of cirnos is the simple front line of spear men, marisas is the back bone of lethal musketeers and grenadiers, more expensive but more firepower
so why in the heck you didnt include my sanae lol shes the commander of everything she is above to... the formation would be, headquarters the moriya shrine with sanae 20$, Nitori 10$, 1 marisa as the commander of infantery (cirnos and marisas) 15$, patchouli 25$ and aya 10$ somehow with this group we can formed a leader group, and here in the headquaters we got just 25 cirnos to defend around the place, it should be enough thats 15 so for the headquartes is 155$
now we got for some rent the 2 barracks which are hakurei shrine and the scarlet manor, they dont want to be colonized by a little man that speaks weird, also reimu needs the money and for just 30$ she would join and leave us use the shrine, the manor alone is 30$ the girls dont want to get involved beside we already got patcho and sakuya, so we leave an small contingent in the hakurei shrine with 20 cirnos and 10 marisas thats 250$ and for the manor we get 30 cirnos 15 marisas and 1 sakuya, thats 425$
so we get in total 830$ the rest is for logistic...
strategy is simple obvious since we are outnumber by a lot, just plant bombs where we think the enemy will be, and always try be ahead of the enemy, they will have it rough since they dont have globes or something that flies to recognise the terrain, so they will have yes or yes to explore by foot, and there is where we can get huge advantage, and just mermaid their forces till they retreat or something else dont know,
now i dont know if we consider or not special abilities, i mean, yukari can open a portal, thats too OP, the gensokyo campaign for napoleon would end faster than me in lunatic mode... also i consider multiplying some characs cause obvious even if you hire them all still dont reach the 1000$ budget