no drive tuning will affect supercruise handling, and 99% of your travel will be in supercruise.
thermal load of d-class thrsuters is quite low, so i don't see a problem with a G3 dirty drive tuning - the only thing which might be the case is your ship might run a bit hotter on high G planets (my DBE with G5 dirty drive tuning and A class thrsuters does so...), and you probably can't highwake from proximity of a neutron star/ back hole.
i would simply give it a try at achenar 3 (6,7 ? G) and at jacksons lighthouse or the black holes at dabih minor- if you can land and start on achenar 3, i don't think you will have a problem anywhere, and when you can low wake from jacksons lighthouse or dabih minor, you sholdn't have a problem on your travel.
unusual ship choice, grats to that! i personally couldn't stand a cutters supercruise turning on such a long travel.... but fly, what you enjoy!