Regarding the negative (historical) trust, unfortunately for us, there is no formal way on bitcointalk to open a dispute or request re-evaluation. One person who have rated us negatively passed away (RIP) and the rest are either inactive or do not reply. So, looks like we will have to keep moving with it and just keep up with hard and decent work.
Quoting this old post for a reason. Currently you have 3 negative feedbacks. Based on the above reply, two of them isn't reversible. But the 3rd active negative feedback is from ‘Jawhead999’ who is a regular forum member. The feedback was made based on the accusation of user Nomercy. He (Nomercy) locked his accusation thread when DuckDice team has paid him some lossback again. I can see that you have reached some reputable forum members to review all of the accusation which was made against DuckDice: Duckdice Reputation ThreadBut have you ever tried to reach Jawhead999 to recheck his given feedback?
I don't think we have actually, I'll8 look into it and see if he will reconsider. I think it's fair to say we've not done our best job in keeping track of all these individual accusations and issues or consistent approach to it all but we certainly are aiming to improve that so I'll see if this user will consider us on that basis.
But very enticing reward program is offered there through the levelling system. 
. BTW, at the bottom of the page I can see this
