I usually take out any effects on the DT and reprogram them in my DAW. I use them mostly to give and idea of what I want them to sound like, but you’re right, if recorded too, they make things more difficult.
Although some times, if I use a big reverb on a specific hit as a variation, or play with tape delay time creatively, I record that for sure, but never an “ambience” reverb, for that I will use a send on Ableton later on.
For working with longer stems, there is usually a phase of listening and picking loops that I like, and then building parts of the songs with them. The crossfade in Ableton is a great tool to make transitions much smoother. And it pays of to have a cool 4 mins of synths you actually play to put in your track.
But I also make sure I record “safety” parts with open filters and no effects.
Actually I love this workflow, it make me feel like a film editor somehow