As I am not a specialist for police nor for Baden, I will just take from Radeckes book which is not allways fully clear:
The Schutzmannschaft is evidently a royal force used in the cities and larger towns. Beginning in 1886, new helmets were issued which had the "Beamten"-spike (the rounded spike similar to the Prussian police model). In the eight largest cities these had the normal Baden "Greif" (as on military helmets) and chinscales "on hooks" (probably using the M87 hook). These had yellow metal parts.
In the other towns and cities, the variation with the mirrored "F" and crown was used. He writes that this was normally silver. The officers helmets had gilt parts with "smooth spike on cross-plate" (here he referres to a picture showing a normal military-style cross plate and straight, pointed spike) and chinscales with slotted screws. Except for the spike, this officer model resembles Slims helmet.
Then he states that the ranks Schutzmann, Sergeant, Wachtmeister and Oberwachtmeister use brass plates and parts, and black leather chin straps attached by hooking. This sounds like my helmet.
So I dont know which ranks actually used the silver plate. He also continues that variations are known with silver "F"-plate and chin scales.
The Gendarmerie force was founded in 1829 basing on the previous "Polizeigarde". They used a great variation of head gear over time, but also turned out using spiked helmets after 1887. These had round spike bases and normal pointed spikes, with the Greif front plate. There is no information when excatly the Schutzmannschaft was split off as separate unit.