Need some help - IV./KG76 & III./EKG1

I need some help, guys. I've fallen into a pit of confusion.

This all started when I began working on a model Me 262 with decals F1+DA. Quick research told me that F1 was the markings for KG76. Deep research of KG76 says they didn't use Me262s (although I found some evidence that they MAY have had some). Anyway, we'll circle back to this...

F1 was also used for StG77 apparently but I don't think that's important here.

Moving forward, I began a project to display all aircraft that had been used by KG76 along with some info about the unit. The Wikipedia page for KG76 mentioned "photographic evidence" of KG76 using He 111s, but I didn't have access to the book that was cited so I started a DEEP search of the internet. With my wife's help, we discovered a single, drawn, side-view image of an He 111, marked with F1+NW. HUZZAAAH! we thought....

The picture has a caption that says, Until December 1944, the F1 codes belonged to IV./KG76, which transformed to the III./Erg.KG1 at that time.

I knew that IV./KG76 changed to a different unit in Dec 1944, but didn't investigate because I was under the impression F1 just STAYED with KG76. However, a quick search showed that apparently yes, EKG1 (Erg.KG1) used F1 markings on their aircraft...This means the information on Wikipedia is almost certainly wrong and the "Photographic evidence" was likely an He 111 belonging to EKG1.

So now, a light goes off regarding the Me 262. I almost GUARANTEE it belonged to III./EKG1. I have found information that says EKG1 was using Ar234s and Me262s.

But wait...if EKG1 was only using Me262s and Ar234s...why would they have an He111? It's December 1944 and they're creating a new unit using jet airplanes...why would they have a very early bomber tossed in the mix? So...uh...circle back and I'm just baffled.

Did KG76 use He111s?
Did Me262 (F1+DA) actually belong to KG76, or was it in fact part of EKG1?
Does anyone have the book referenced in the Wikipedia citation: Bomber units of the Luftwaffe, 1933-1945 : a reference source (volume 2) - ISBN 1903223873

BONUS INFO:
Heres a link to a post on this site discussing F1+DA and not really reaching a concrete conclusion.
Here's a link to the He111 F1+NW image
Here's a link to a page with some info about EKG1
Here's a link to a page with some info about KG76
Here's a discussion on this site regarding the F1 code being used in both KG76 and StG77
Here's a listing of unit codes showing F1 being used on KG76, III./StG77, and IV./EKG1