Hi, Dan...
Thanks for posting these pictures... they are very nice
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I would suggest that this is an He111H, possibly an early sub-type, perhaps an H-1 or H-2 given the layout of the intake on the right side of the engine cowling. You can see that it is relatively close to the wing; later versions tended to have longer, more noticeable intakes.
The code 1G+GE suggests the Gruppenstab of IV.Gruppe/KG27. My understanding is that the fourth Gruppe of a bomber unit was quite often the training Gruppe, and this may be why the machine does not appear to carry a bomb sight. Certainly, I can see no fairing for the bomb sight in the usual position under the nose.
If this is a Gruppe staff flight machine, then the second letter 'G' should have been green RLM25, and the spinners would likely have matched this colour. To my eye, though, the colour of both letter and spinners seems a tad light to be this shade, and although I would not discount this coding as being 1G+GE, I'm not sure from my first look at the photo. I did wonder if the last letter was instead perhaps an 'L' rather than an 'E'. This of course would make it a machine of 3.Staffel/KG27 and might better account for the light shade of the I/D letter and spinner, as they would normally have matched the 3.Staffel I/D colour of yellow in this case. I am happy to be informed otherwise, though.
Kindest regards,
Paul