It's already been done, and it's more like $6 (even less per unit if buying in bulk). The 1000uf caps are an issue though. They are really close together, so the size is important. Only the 2000 hour caps will fit in there, which will be fine for about 7 years with your current workload, and even then, only the 1000uf caps would need replacing. Assuming a 70C average temperature. Get them from Digikey, Mouser is out of a lot of things, including some of these caps.
SHTechnics posted this in reply #413 (and I added two edits):
C1- 82 uf 400v --> RUBYCON 400BXW82MEFR18X25 Electrolytic Capacitor, Miniature, 82 µF, 400 V, ± 20%, Radial Leaded, 12000 hours @ 105°C
C2 - 10 uf 50v --> NICHICON ULD1H100MDD1TD Electrolytic Capacitor, 10 µF, 50 V, ± 20%, Radial Leaded, 10000 hours @ 105°C (I changed this to a longer life cap)
C7 and C8 - 1000 uf 35v --> RUBYCON 35PX1000MEFC10X20 Electrolytic Capacitor, Miniature, 1000 µF, 35 V, ± 20%, Radial Leaded, 2000 hours @ 105°C (changed to a higher temp cap)
C10 - 470 uf 35v --> NICHICON UPW1V471MPD1TD Electrolytic Capacitor, 470 µF, 35 V, ± 20%, Radial Leaded, 5000 hours @ 105°C