Strictly speaking the lounge dragon would be right since you buy a cheapie on the basis that you cannot change anything. If you want flexibility you have to shell out cash.
Logically, changing a flight generally won't cost KLM anything since they have a seat available anyway.
On the other hand, if the flight you are originally booked on is fully booked , they might lose out on selling another seat on that flight; which seems why they restrict the cheapies so heavily.
That said, it is extremely strict and rather customer unfriendly. I have experienced problems with this myself, but I was lucky to have found a person who wanted to tread outside company policy to rebook me. This is the key issue, you will have to find someone who is 'nice' enough, which you implied by using the term 'lounge dragon'.
In my experience you'd be best off talking to an older member of staff, a member that still remembers the time when there was still flexibility in customer relations. Start off with a smile and you should be alright.