The Redcaps are already armed. They have guns. They just aren't armed as House Guards are, ie, they aren't our own private army with top-of-the-line gear. The equipment they already have was sufficient to fight the Mob on the Mob's home turf; why would it be less effective now?
Their equipment was enough to ambush the
unprepared and
outnumbered Mob, while working alongside the Sharks who's
singular goal and focus was driving the Mob out. Even then, it was only because we spent
multiple turns producing healing potions, that there were no casualties.
Which means, the Mob, who were outnumbered, unprepared,
and ambushed, still were able to do enough damage to make it a Pyrrhic victory if we didn't have those healing potions.
While we've been recruiting people to the Redcaps, we now have much more territory to defend, which means that our rifles and veterans are spread out among our territory. While that is more than adequate against common thugs, it would be vulnerable to the same tactics we used to drive the Mob out. An ambush of a numerically superior force, armed with powerful ranged weaponry, at an unexpected time/place.
Giving the Redcaps House Guard level equipment should not only ensure that our weapons are of a higher quality, but it should also make sure that they have health potions on stand by, making it even
harder for an attack against them to succeed.
And your protests about not having money to buy additional income continue to ring false because we absolutely have money to buy additional income. We have access to up to 12 Clean Terra (if we liquidate Essence Pearls; 6 if we don't) currently, which is enough to do all but one of the Investment options.
Liquidating the pearls
is an investment option, so we only have 6 Terra to spend this turn, as we can't take two actions in the same category. The most we can get for that is an extra
2 Terra of clean income, which also costs our only remaining Innumerable Aspect Favour. Constantly running our budget to the limit isn't a good idea, as the income comes at
the end of the turn. And while people have accepted partial payment upfront in the past, it is a much harder sell to accept
no payment upfront.