My understanding is that these are shoulder boards for a Medical Assistenzarzt (Leutnant), and I'd like help confirming that. 

Also, how do the pips work if they're different? One is large and gold, one is small and bronze, and two are small and silver, and none seem alike. 

Well the White metal ones are Pips for Noncommissioned Officers. it's the Gilt Pips Officers had.

 

The shoulder boards themselves look alright, will let oters look see though.

 

Here's  pairs for sale.

https://www.imcsmilitaria.com/shop.php?code=61511

https://www.emedals.com/a-german-army-medical-administration-shoulder-boards

Medical Staff (Arzt) should also have a snake on a stick device in addition to the pips.  Your board may be Transportation of something else and the mixed pips do not seem to be correct for Medical.  

 

 

Nachschub et al has Light Blue or in German Hell Blau Waffenfarbe. With the mixed up Pips, it's possible the original pins on it were removed long time ago, and these were added with what was laying around.

 

A Major of the Nachschubtruppen, a Waffenrock, note the Hell Blau Wafenfarbe throughout.