Maybe, just maybe, you can get the module to work without a reboot. This particular uplink module is configurable to 4 x SFP or 2 x SFP+. You configure it this way:
set chassis fpc 0 pic 1 sfpplus pic-mode 1g
or
set chassis fpc 0 pic 1 sfpplus pic-mode 10g
Perhaps changing this and committing will make the switch query the hardware again to see if there's a module in there. I seem to remember having done this without rebooting, but I may be wrong. I'll try it on an EX3200 with the 4x1 G module (not reconfigurable, but still).
Edit: I hot-plugged an EX-UM-4SFP module into an EX3200-24T running 14.1X53-D40 and it didn't need a reboot! I can ping my network from the switch and all, so not just link on the interface. Now, the EX4200 is a different switch and it has a separate PFE for the expansion slot, which the EX3200 doesn't.