I think I’ve finally found a suitable mercenary replacement for the Teutonic Knight; the Geschwindstück (thanks to HoopThrower for pointing it out).
I always pictured the Geschwindstück as the perfect option for an Artillery Mercenary. It was a weird, highly specialized gimmick gun that only could be afforded by rich states.
So instead of the Prussian Company that I initially suggested below, a Saxon Company could replace it with Teutonic Knights being swapped for Geschwindstück.
Prussian Company
Consists of Giant Grenadiers and Bosniaks, and Teutonic Knights. The current prospects for a Prussian civilization are slim, but they could get a little recognition with a mercenary company.
Despite their Balkan origins, the Bosniak Corps actually served Prussia.
Teutonic Knights would be a new mercenary to complete the company. As a nod to their AoE2 counterpart, they should be a swordsman with ridiculously high melee armour. They could also possess some of the same abilities as Hospitallers.
Saxon Company
Consists of Giant Grenadiers, Bosniaks, and Geschwindstück. This would be a mix of mercenaries (and other extravagantly expensive units) that fought for Saxony and Prussia. Technically a name like Brandenburgian/Brandenburger Company would be more accurate, but that’s a mouthful and it also has some not so nice WW2 connotations.
Geschwindstück means “quick-fire gun”, so obviously a rapid rate of fire would distinguish them from other artillery. Their unique method of reloading by tipping the barrel almost vertically would also make them stand out. Their rapid fire would make them a very powerful unit, but they are also described as expensive and vulnerable to damage, so a high cost and low health could balance very high DPS.