IMO a valid point to the weakest side of the XY, the Tonverk does amazing drums due to multiple stages of compression, waveshapers,, bit reduction and distortion via insertFX and buses..
Thedigitakt has drive pre- and post-filter if Im not mistaken and each sound has these per step along with bit crushing.
Im very much hoping TE address this in the future OS at 2300 It’s kinda expected ..
IMO your best bet is to setup the limiter /clipper /saturation; along with lofi and drive FX and treat /resample each drum hit as your setforth a desired effect.. and thus rebuild your drums though via a resampled kit.