Hi Scott,
I would be surprised to find that the standard GC's worked well with headphones. I would think that a modified device would work well though. I have them on my phono cartridge and tape deck heads and preamps. These are special designs of course, using far less of the materials than the standard GC's are built with and hand tuned to suit the particular purpose.
Headphone amps might be a place to try, but I would only recommend a standard RCA, perhaps plugged into an RCA to tip and ring plug adapter. I have made tip and ring GC's for an M Audio outboard DAC that worked quite well, but we haven't elected to make a niche product like that available.
I can probably get authorization to build and sell prototypes and special production orders. I haven't yet asked about this format for GC's. I am under some legal constraints about what I can and cannot do with GC's, just to get them to market.
Bud