I think I found an appropriate capacitor:
Manufacturer: Murata Electronics North America
Manufacturer Part Number: ECASD91B107M012K00
Description: CAP ALUM 100UF 12.5V 20% SMD
Lead free / RoHS Compliant
However, SMB packaged diodes for some reason aren't the same size as the one I measured on the board. It appears to match an SMA packaged diode.
I found this diode which appears to be the correct size:
Manufacturer: Diodes Inc
Manufacturer Part Number: S2BA-13-F
Description: RECTIFIER GPP 100V 1.5A SMA
Lead free by exemption / RoHS Compliant
Is there anything glaring that would suggest why either of these won't work (I'm a mechanical engineer normally so I don't have a lot of electronics experience)?