From my initial parts grope, here are my suggestions:
1. compared to the eagle, there is a small tubular structure on the bottom. Don't even bother cleaning the resin parts up. Build one either out of brass rod, evergreen rod, or a suitable wire. If you're really uncertain about your scratchbuilding skills, even sections of brass rod cut to the correct lengths with squared off ends superglued together will look better than trying to clean up the resin parts.
2; The engine bells are direct copies of the plastic model kit. You should thin those out from the inside and plan on either painting them with alclad or applying bare metal foil to them. There are some detail issues with those engine bells, so if you're really ambitious, scratchbuild new engine bells and apply correct details. IIRC, that involves the pre-heat fuel tubes going to & from the bells.
3. ignore the old school guys who scream and yell about resin copies of out of production plastic kits. if someone wanted to re-pop the kit, they would have by now.The ones that scream the most don't have credible arguments, they just say its wrong.
4. the beak is not exactly right. reshape the end of the command module so its accurate.
5. After that, as you said, check your references, there are a bunch of details you can fix.