Anyway a proper pipeline I use for years is:

+proj=pipeline +step +inv +proj=krovak +lat_0=49.5 +lon_0=24.8333333333333 +alpha=30.2881397527778 +k=0.9999 +x_0=0 +y_0=0 +ellps=bessel +step +inv +proj=hgridshift +grids=Slovakia_JTSK03_to_JTSK.gsb +step +proj=krovak +lat_0=49.5 +lon_0=24.8333333333333 +alpha=30.2881397527778 +k=0.9999 +x_0=0 +y_0=0 +ellps=bessel +step +inv +proj=krovak +lat_0=49.5 +lon_0=24.8333333333333 +alpha=30.2881397527778 +k=0.9999 +x_0=0 +y_0=0 +ellps=bessel +step +proj=push +v_3 +step +proj=cart +ellps=bessel +step +proj=helmert +x=485.021 +y=169.465 +z=483.839 +rx=-7.786342 +ry=-4.397554 +rz=-4.102655 +s=0 +convention=coordinate_frame +step +inv +proj=cart +ellps=WGS84 +step +proj=pop +v_3 +step +proj=webmerc +lat_0=0 +lon_0=0 +x_0=0 +y_0=0 +ellps=WGS84

It is the official pipeline provided by our national cartography office, together with Slovakia_JTSK03_to_JTSK.gsb file. Without this pipeline the offset varies up to more than 10 meters. With the pipeline the transformed geotata matches that from state office's WMS 🙂

It makes slightly more sense, but still seems dubious to me

The part "+step +inv +proj=krovak +lat_0=49.5 +lon_0=24.8333333333333 +alpha=30.2881397527778 +k=0.9999 +x_0=0 +y_0=0 +ellps=bessel +step +inv +proj=hgridshift +grids=Slovakia_JTSK03_to_JTSK.gsb +step +proj=krovak +lat_0=49.5 +lon_0=24.8333333333333 +alpha=30.2881397527778 +k=0.9999 +x_0=0 +y_0=0 +ellps=bessel" is what you would want to apply to go *from* "S-JTSK / Krovak East North"   to  "S-JTSK [JTSK03] / Krovak East North"

and then the second part uses the expected Helmert tranformation from "S-JTSK [JTSK03] / Krovak East North" to WGS 84, so this pipeline is to go from "S-JTSK / Krovak East North" to WebMercator WGS 84.

Perhaps your dataset is mislabelled as being in "S-JTSK [JTSK03] / Krovak East North"  whereas it is in "S-JTSK / Krovak East North"  ?


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