Looking at the internal pics, it appears to be a standard shielded USB type B connector for PCB through hole mounting.  There are many of these available from vendors such as Mouser, here's one example (not sure if this particular one would work however):

http://www.mouser.com/ProductDetail/FCI/61729-1011BLF/?qs=zxzm42eeoPOXEPDZb4guCHr4XXm7q9HTzfbn0yXAQl4%3d

The part itself will cost well under $1.  However, making sure a replacement would fit will be more difficult; if the manufacturer and part number are not on the part, I doubt Line 6 would tell us the manufacturers part number of the jack.  If a tech knows what he is doing, he can measure the HD PCB and cross reference with different connectors' data sheet dimensions until he finds a suitable replacement that will fit the PCB and case opening, and has the proper pin configuration.

Another issue would be to find a technician competent to remove and replace the part; the PCB is what is know as multilayer (multiple layers of copper conductors inside of the board that are invisible from the outside).  If a technician does not know what he is doing, he can ruin the PCB by damaging a component pin hole while removing the old part.  The board would then possibly be destroyed.

I went through something like this when the pad switch on my old XT Live was broken, could not at all get part info from Line 6.  But I was successful finding a replacement and installing it, then again I have been designing equipment PCB's for decades, and know how to specify parts to go on a PCB as well as repair them properly.

In summary, it would be possible to have a non- Line 6 tech fix the board, but he will really need to know what he is doing.  It might be best to get the repair quoted by Line 6 if you do not know someone competent to do the job.

EDIT:  Another thing you could try; if you have the part that broke, you might be able to carefully superglue it back.  I'd try using gel superglue, use it sparingly, and carefully dry fit the broken piece before regluing it.  Use just enough glue to hold the plastic where it separated, and try not to get it on the pins in the jack.  Also, after fitting the part, wait an hour or so for the glue to fully set (superglue is supposed to be quick drying, but it's better to be safe than sorry).