Well, I don't know about 109Fs, because I seem to recall JG1 switched to 190s pretty early on. I don't know of any profiles, but I stumbled across
this webpage that shows a wartime photo of a 109F(?). However I've seen a few profiles of 109Es.
There's the 1939-era green/green scheme visible on some E-1s (and probably was used on E-3s/4s as well, albeit breifly).
If you're not sure what I mean, look
here Here's an E-3. It doesn't look accurate, as I don't think any 109Es had a solid, single-color, grey upper surface. However it supplies a name and date, which you can use to search more.
Wartime photo with the description:
"Lt. KNOKE's Bf 109 E, black 3, Autumn 1941. It show the I./JG1 "Laughing sun" on motor and "Lilo". While "Losigkeit" Jagdgruppe mission all personnal marks where over-painted."
This page has more photos including the crashed plane.
I've got only 1 color profile from a Gunston book. I'll scan it in the morning and post it for you. It's a high-backed green/green Emil with a yellow nose and no side mottling.
Maybe a little late for your timeframe,
this page has an image and description of a G-6/AS from JG1 (scroll down a bit it's there on the left side).