Larry:
Sorry, but I have no aswer. If Schmid's FB will be sometime found, then it will help.
Regarding Your questions on I./ZG52 / II./ZG2 claims:
Yes, documents are lost. So, we could go on other way.
Claims were scored by pilots. And (at least some of them) were added to their official score.
II./ZG2 sustained seems the lowest losses among all Gruppen during BoB (idf we will not cound I./ZG76

). It will help a bit. Some of claims could be filed to them, but we will never know how many.
Uffz. Karl-Heinz Hoyer (MiA)
Uffz. Max Schuler (MiA)
Uffz. Heinz Conrad (KiA)
Maj. Harry Carl (KiA)
Oblt. Ernst Hollenkamp (KiA)
Lt. Jurgen Meyer (KiA)
Hptm. Adolf Schuldt (KiA)
Fw. Lorenz Beil (KiA)
Uffz. Hermann Deuker (MiA)
Lt. Hans-Dietrich Albert (KiA)
Lt. Karl Stix (PoW)
Lt. Schunemann (KiA)
Oblt. Willi Brede (PoW)
So, for all Battle of Britain only 12 pilots were killed. That mean, the rest survived and were to became Night fighters with 4./NJG3. Yes, probably, some of them refused to be nightfighters, and were transferred to other units. Then, some of them were later transferred to other NJG Gruppen.
I think, Larry, that it is worth to look in NJG units and it's pilots so find out who survived BoB with II./ZG2, and how many victories each of them got prior to NJG. Hans Schmid is just an example of one of them. Other were - Hoffmann, Elstermann...
For example:
Kurt Loos, served with ZG2 in 1940, and later with 2./NJG1 and later with NJG5. Had 13 night victories. Had DKiG. But who knows, may be he had some claims before became nightfighter... I know, it is bad method, but if You will check early 4./NJG3 pilots list, You will find needed men. Those could have 1 or 2 or 3 claims with II./ZG2 in 1940, but is is better then nothing.
Hptm. Peters, who came to lead I./NJG3 (former V./LG1) and later became StaKa of one o Staffel within that Gruppe, is known to came from ZG2. Was he a StaKa of 4./ZG2 in later stages of BoB? How many claims he had?