Here's something to consider.
Lower the board that the drag chain is attached to by 4" or so to increase the bend radius of the chain. Then add a second board just above and ahead of where the cables come out of the chain, but position it just below the bottom of the gantry so the gantry can't hit it. Bevel the end of the second board so that the chain can't snag on the end of the board. Now the chain can slide onto the second (higher up) board to provide sag support for the chain only when the chain needs it. You'll need to find the right place for the second board by watching how the chain lays onto the board with no interference of any kind. The second board could even be installed on a shallow angle if it works better that way.
I have a 12' long DIY machine that has problems like this and cured it with just a piece of MDF stuck into the end of the cable channel I made for it from steel angles. It still sags too much and I have intentions of trying this second level of support idea after I finish building a heavier duty frame for the machine during the fall and winter months.
I have been into a manufacturing business near Fort Bragg that has a 20' laser cutter table for parachute cloth cutting. It appeared to be a commercial machine but I wasn't able to see how the cabling was supported. Could only see it from a distance.