Thank you for your output with verbose and debugs turned on. It seems the device is failing to respond to the very first byte of data being sent to it. We haven't even got as far as addressing the instrument.
You did confirm earlier that ATN was being pulled low. From the output we see a timeout has occurred when sending the NRFD signal during the handshake while sending the first byte. From the preceding steps in the handshake process we can surmise that NDAC was low, indicating the device was at attention and NRFD was high, indicating that the device was ready to receive data. The AR488 interface then placed the first byte (3F) on the bus and asserted DAV (data available). However, the instrument does not respond by asserting NRFD to indicate that it has accepted the data.
Since you said that you checked the wiring several times, one would have to presume that it wasn't mirrored as wkd suggested, i.e looked at from the opposite perspective, and that all wiring, including ground was correct. In which case, the instrument is either not detecting the DAV signal, or else not replying to it to say has read the first byte (3F) from the GPIB bus. This might suggest that the GPIB interface on the instrument may be faulty or simply not ready to receive data for some reason. Trying the AR488 on another instrument would confirm or rule out the GPIB hardware on the instrument side of things.
You can also try the ++xdiag command as described at the very end of the manual, without the interface being connected to the instrument. This allows the status of each signal to be set and flipped to confirm that the GPIO pin is working correctly. Bear in mind that the effect of the command lasts about 10 seconds before the line state reverts to the interface default. Its a bit tedious to do with a DMM, but it would prove whether all the GPIO pins on the Uno are working as expected.