Because of lack of OpenOCD support I haven't done much thinking around cJTAG. As you point out, cJTAG is significantly more complex than JTAG. I was also unable to find a debug device that we could use instead of the OpenOCD-supported ones that would allow for low-level cJTAG control. (If one exists, please point it out!)
That doesn't really solve your problem, though.
I'm open to adding some kind of 2-wire DTM to the debug specification. High speed I2C is probably suitable. That does leave you with the problem of connecting it to gdb. The software implementation is probably not too hard. The hardware implementation also seems pretty doable. A board with USB, a bit-banging microcontroller (or FPGA), and a few GPIO pins should be enough. (RISC-V on an FPGA with some custom instructions would be a cool implementation.)
Would anybody be interested in pursuing this path?