Most of the heat on these is dissipated through the rear of the regulator, into the pcb. It might help to stick a heatsink on with good thermal adhesive, but I'm not sure how much good it would do.
Space is restricted, but a more effective option might be to fabricate a custom heatsink 'paddle' from thin copper sheet and solder the tail of it to the tab of the regulator, or even between the regulator and the pcb - bearing in mind that it will be connected to ground, so shouldn't be allowed to touch anything else on the pcb.
I would still favour the larger regulator attached to the metal casing. It would mean a bit of faffing about, and the part is harder to find, but Mouser have them in stock.
It's also a shame they don't make a 2 amp version of this device... they do for other voltages, but not 8 volt.