I tried manipulating a large diameter trimmer cord in a detergent solution over several days in a row, then, as a last resort before rerouting the drain hose, I straightened out a coat hanger. I inserted the end with the spiral twist and worked it back and forth and rotated it against the clog. . . and finally it broke up and started to drain. I wasn't sure the rubber drain tube would survive, but it did!Have no words on the Drano and where it ends up and what it does when it gets there.......
Have you tried some larger diameter string trimmer cord? Several sizes are readily available.
I would get the largest that is available(or try what I have), cut it to a length several inches longer than the current plug spot, and put it in an electric drill. Feed it down while running the drill at low speed. Probe the plug, pull back, probe... rinse repeat. It might not hurt to add some vinegar(Drano is a base, vinegar slightly acidic) while running the drill. It may cause foaming. It may also cause foaming down the drain, and break things loose.
This is a process that may take some time, but should get there if you are patient. If it is plugged with stuff that turned to dirt, the dirt should absorb liquid, become mud, and be visible when you withdraw the string to check progress. Either way, it was once mixed with water, and should mix again. Unless someone put some Portland cement down the tube... or some gasket forming 'stuff' or ???