It could be the white point conversion at some point from the CST (which you could turn off, but this case should leave as default) I believed in ACES(the actual working space), it is D60 (regardless of the white point of selected ODT which conversion will apply at the end). So when using the CST, since Rec.709 uses D65, there will be a white point conversion applied automatically back and forth which everything should turn out fine if CSTs on both end are set correctly.
Then It could be a warmer white point from the Film Print LUT that you’re using (hence “D60” in the naming). Which I think is close to what the actual prints on the projection would give. For creative purpose you might want to go with the D65 version of the LUT if you want a cooler white.
Using a LUT this way. It is important that you’re aware that the result is based on the empirical data that’s derived from the LUT which the color volume of the resulting image will be limited to what the output color that LUT gives out. (This case Rec.709)
On the conversion, since the print LUT is expecting a film scan image, converting to “Rec.709/Cineon”should get you a better result.
But I would just ditch the CST and use the ACES transform OFX instead, converting from ACEScct to ADX10 then apply the LUT then another ACES transform converting the Rec.709 result back into ACEScct.
This should give a better match because it uses the appropriate math reversing the ACES RRT/ODT when converting back from Rec.709.