Most importantly, you can definitely improve your sound with some modest upgrades. Based on your budget you may want to consider looking at your cables, power cords, connections. Spending money in this area would boost performance of your entire system. As it relates to components I have not heard the Chord but have had Lumin in my system...D2 and T2. What if you traded in the Chord and Lumin for a newer Lumin that does both (as others have suggested). I think that is what I would do if it were me. If you like the Lumin sound going up in their range only gets better.
Let us know how you make out!