Personally, I've never had an issue with oils and KCCC. I've used straight oils as a leave in, Donna Marie L&T, KBB Hair Milk, and loads of others without so many oils. SheaM, Knot Today, Giovanni Direct LI (may contain oils, not sure). Regardless all of these leave-ins have worked for me with KCCC.

If your hair likes oils you may want to try the Aubrey Organic's White Camilla. It's more oil-heavy than the AOHR. I have the tendency towards dryness (probably not as much as yours) and this will weigh down my hair if I use it too much. Regardless, it's a great moisturizing condish and I love it as a DT.
mostly 3a/some 3b/2c at the nape
med-coarse and porous
Current routine:
Cleansing: Co-wash with V05, JCCC
Leave-in: KCKT
HESMU, Joiwhip
Protein Treatment: Ion effective care treatment