The speaker modeling affects only the DI output in "post" position, which is post power tubes. It is not a bad thing, it's simply eq'ing the DI output (and yeah, it might be a digital eq - don't know, don't care) so you get a curve emulating what you'd expect from a well-mic'd speaker cab. It only effects the DI output, nothing else.
The "modern" OD channel is only modern in the sense that it has active eq, and the eq is solid state analog. But the OD channel still has a tube vibe - it uses the same 12AX7 (V1) as the passive channel for its first stage, but it has a solid state final stage whereas the passive channel uses the other half of V1 as its final stage. However, the OD channel can be "more tube" than the passive channel. On the OD channel if you set gain to 0 (if you want a clean sound) and blend on 10, you are now going through 3 tube stages in the preamp - one half of 12ax7 V1 as the first input stage, and both halves of 12ax7 v2 in the overdrive circuit - whereas the passive channel has two tube stages - one half of V1 as the first stage, the other half of V1 as the final stage.
Personally I think you're stressing over nothing. Having active solid state stages, or even dsp, in the preamp section is not going to make a tube amp suddenly sound digital. The real key to the sound of a tube amp is the power tubes imo. Solid state power amps with tubes in the preamp just don't sound tube to me. But add a tube power amp to a solid state or digital preamp and you've got a tube sound.