You give a good argument to stick with the King James.
Regardless of how they are translating this, whether responsibility, or stewardship, or "still something", it's from oikenomia, "house law", that is, the manner of running a household to provide for the needs of the occupants. The "dispensation", that is, the dispensing of what is needed for the household.
And in fact there were various ways employed by God towards taking care of the Humans He had made. In the garden, God gave man 1 rule. When he disobeyed, God gave a new set of rules. After the flood, God gave Noah different rules, one's He had not given before.
Each of these are a change in God's manner dispensing grace and justice to man. When God gave the Law, the rules changed, and this is a despensation.
Dispensations are written into the Bible, there is no way around that fact.
Much love!