I can't really see how printing the internal structure of a part in a curved manner would help at all. The base of the part is still flat and when you build the part up to level, the shrinkage would be the same and so would the curl of the part. You could try a convex print bed, but the lift varies depending on the size and shape of the part so this would be difficult.
You could try printing ridges which would have a chance to cool, then infill later, but you would need a nozzle that could reach down into a groove without hitting the plastic ridges. I have tried printing parts with a ridged base, where the ridges gradually meet off the bed about 3mm up on the part and this does work OK and is an option when printing large parts which are for functional purposes only. This is really a similar method to using a raft.
The use of a heated bed, on Kapton tape cleaned with acetone seems to do the trick. I have also used ABS juice on glass which also works well. If you are getting bad curling problems I suggest you check the actual bed temperature with a infra red thermometer and have a look at other methods.
