Inecto is a very lightweight cheap conditioner available in a number of countries including the US. Ignore straplines and sales pitches, it contains very very little oil, to the point I cannot even tell it's there, it's nowhere near conditioning enough for my hair. It is amazing as a CO-wash, gets even heavy coconut oilings out, leaving my hair 'squeaky' and makes a great base for intensive treatments.
If you cannot get any oils out without sulphates then either you are not using enough product, a conditioner that focuses too much on moisturising ingredients and not on cleansing agents (cationic surfactants), poor co-washing technique or you have something else in your routine that the oils are gumming up with. Heavy butters are a different matter, many find them a nightmare to get out and most don't actually 'nourish' hair anyway.
Other than that TBH I don't understand what you are looking for. What ingredients are you willing and able to use? If you take natural oils out of a conditioner and any plant extracts that might irritate, you aren't left with much you would recognise as a natural ingredient! Just the lab manufactured fatty alcohols, cationic surfactants, preservatives and the like.
There are JASON and Aloe Pura brands of aloe vera conditioner but both are packed with plant extracts and other ingredients any one of which could irritate. Otherwise you could go online and purchase a conditioner 'base' - that would have few ingredients but is not in store.